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On the smoothness in the weighted Triebel-Lizorkin and Besov spaces via the continuous wavelet transform with rotations J. Pseudo-Differ. Oper. Appl. (IF 1.1) Pub Date : 2024-03-15 Jaime Navarro, Victor A. Cruz-Barriguete
The main goal of this paper is to show that if \(u\in W^{m,p}(\mathbb R^n)\) is a weak solution of \(Qu = f\) where \(f \in X^{r,q}_{p,k}(\mathbb R^n)\), then \(u \in X^{m+r,q}_{p,k}(\mathbb R^n)\) with \(1< p,q < \infty \), \(0< r < 1\), k is a temperate weight function in the Hörmander sense, \(Q = \sum _{|\beta | \le m} c_{\beta }\partial ^{\beta }\) is a linear partial differential operator of
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Uncertainty principles for the biquaternion offset linear canonical transform J. Pseudo-Differ. Oper. Appl. (IF 1.1) Pub Date : 2024-03-15 Wen-Biao Gao
In this paper, the offset linear canonical transform associated with biquaternion is defined, which is called the biquaternion offset linear canonical transforms (BiQOLCT). Then, the inverse transform and Plancherel formula of the BiQOLCT are obtained. Next, Heisenberg uncertainty principle and Donoho-Stark’s uncertainty principle for the BiQOLCT are established. Finally, as an application, we study
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Kirchhoff type mixed local and nonlocal elliptic problems with concave–convex and Choquard nonlinearities J. Pseudo-Differ. Oper. Appl. (IF 1.1) Pub Date : 2024-03-15
Abstract In this paper, making use of non-smooth variational principle, we establish the existence of solution to the following Kirchhoff type mixed local and nonlocal elliptic problem with concave–convex and Choquard nonlinearities $$\begin{aligned} \left\{ \begin{array}{ll} \mathcal {L}_{a,b}(u)=\left( \int \limits _{\Omega }\frac{|u(y)|^{p}}{|x-y|^{\mu }}dy\right) |u(x)|^{p-2}u(x)+\lambda |u(x)|^{q-2}u(x)
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The infinite-order integro-differential operator related to the Lebedev–Skalskaya transform J. Pseudo-Differ. Oper. Appl. (IF 1.1) Pub Date : 2024-03-15 Ajay K. Gupt, Akhilesh Prasad
In this article, we introduce infinite-order integro-differential operator related to Lebedev–Skalskaya transform. Some characteristics of this operator are obtained. Furthermore, we establish the necessary and sufficient conditions for a class of infinite-order integro-differential operators to be unitary on \( L^2({\mathbb {R}}_{+}; \, dx)\). Some classes of related integro-differential equations
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A more direct way to the Cauchy problem for effectively hyperbolic operators J. Pseudo-Differ. Oper. Appl. (IF 1.1) Pub Date : 2024-03-15
Abstract This paper is devoted to a simpler derivation of energy estimates and a proof of the well-posedness, compared to previously existing ones, for effectively hyperbolic Cauchy problem. One difference is that instead of using the general Fourier integral operator, we only use a change of local coordinates x (of the configuration space) leaving the time variable invariant. Another difference is
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Wave equations with a damping term degenerating near low and high frequency regions J. Pseudo-Differ. Oper. Appl. (IF 1.1) Pub Date : 2024-03-14 Ruy Coimbra Charão, Ryo Ikehata
We consider wave equations with a nonlocal polynomial type of damping depending on a small parameter \(\theta \in (0,1)\). This research is a trial to consider a new type of dissipation mechanisms produced by a bounded linear operator for wave equations. These researches were initiated in a series of our previous works with various dissipations modeled by a logarithmic function published in (Charão
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Modified scattering for the higher-order KdV–BBM equations J. Pseudo-Differ. Oper. Appl. (IF 1.1) Pub Date : 2024-02-26 Nakao Hayashi, Pavel I. Naumkin
We study the Cauchy problem for the higher-order KdV–BBM type equation $$\begin{aligned} \left\{ \begin{array}{c} \partial _{t}u+i\varvec{\Lambda }u=\varvec{\Theta }\partial _{x}u^{3}, \ t>0, \ x\in \mathbb {R}, \\ u\left( 0,x\right) =u_{0}\left( x\right) , \ x\in \mathbb {R}, \end{array} \right. \end{aligned}$$ where \(\varvec{\Lambda }\) \(=\mathcal {F}^{-1}\Lambda \mathcal {F}\) and \(\Theta \)
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A structure theorem for fundamental solutions of analytic multipliers in $${\mathbb {R}}^n$$ J. Pseudo-Differ. Oper. Appl. (IF 1.1) Pub Date : 2024-02-26
Abstract Using a version of Hironaka’s resolution of singularities for real-analytic functions, any elliptic multiplier \(\text {Op}(p)\) of order \(d>0\) , real-analytic near \(p^{-1}(0)\) , has a fundamental solution \(\mu _0\) . We give an integral representation of \(\mu _0\) in terms of the resolutions supplied by Hironaka’s theorem. This \(\mu _0\) is weakly approximated in \(H^t_{\text {loc}}({\mathbb
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A class of fractional parabolic reaction–diffusion systems with control of total mass: theory and numerics J. Pseudo-Differ. Oper. Appl. (IF 1.1) Pub Date : 2024-02-26
Abstract In this paper, we prove global-in-time existence of strong solutions to a class of fractional parabolic reaction–diffusion systems posed in a bounded domain of \(\mathbb {R}^N\) . The nonlinear reactive terms are assumed to satisfy natural structure conditions which provide nonnegativity of the solutions and uniform control of the total mass. The diffusion operators are of type \(u_i\mapsto
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Existence and blow-up of solutions for a class of semilinear pseudo-parabolic equations with cone degenerate viscoelastic term J. Pseudo-Differ. Oper. Appl. (IF 1.1) Pub Date : 2024-02-12 Hang Liu, Shuying Tian
In this paper, we consider the semilinear pseudo-parabolic equation with cone degenerate viscoelastic term $$\begin{aligned} u_t+\Delta _{\mathbb B}^{2} u_t+\Delta _{\mathbb B}^{2}u-\int _0^t g(t-s)\Delta _{\mathbb B}^{2}u(s)ds=f(u),\ \text{ in } \text{ int }\mathbb B\times (0,T), \end{aligned}$$ with initial and boundary conditions, where \(f(u)=|u|^{p-2}u-\frac{1}{|\mathbb B|}\displaystyle \int _{\mathbb
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Toeplitz operators and composition operators on the q-Bergman space J. Pseudo-Differ. Oper. Appl. (IF 1.1) Pub Date : 2024-02-10 Houcine Sadraoui, Borhen Halouani
In this work we consider Toeplitz operators and composition operators on the q-Bergman space.We give some spectral properties of Toeplitz operators in general and a sufficient condition for hyponormality of Toeplitz operators in the case of a symbol where the analytic part is a monomial. We also give a necessary condition for hyponormality in the general case of a harmonic symbol as well as a necessary
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Geodetically convex sets in the Heisenberg group $${\mathbb {H}}^n$$ , $$n \ge 1$$ J. Pseudo-Differ. Oper. Appl. (IF 1.1) Pub Date : 2024-02-10 Jyotshana V. Prajapat, Anoop Varghese
A geodetically convex set in the Heisenberg group \({\mathbb {H}}^n\), \(n\ge 1\) is defined to be a set with the property that a geodesic joining any two points in the set lies completely in it. Here we classify the geodetically convex sets to be either an empty set, a singleton set, an arc of a geodesic or the whole space \({\mathbb {H}}^n\). We also show that a geodetically convex function on \({\mathbb
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Molecular decompositions of homogeneous Besov type spaces for Laguerre function expansions and applications J. Pseudo-Differ. Oper. Appl. (IF 1.1) Pub Date : 2024-02-10 He Wang, Nan Zhao, Haihui Wang, Yu Liu
In this paper we consider the Laguerre operator \(L=-\frac{d^2}{dx^2}-\frac{\alpha }{x}\frac{d}{dx}+x^2\) on the Euclidean space \(\mathbb R_{+}\). The main aim of this article is to develop a theory of homogeneous Besov type spaces associated to the Laguerre operator. To achieve our expected goals, Schwartz type spaces on \(\mathbb R_{+}\) are introduced and then tempered type distributions are constructed
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An extension of localization operators J. Pseudo-Differ. Oper. Appl. (IF 1.1) Pub Date : 2024-02-10 Paolo Boggiatto, Gianluca Garello
We review at first the role of localization operators as a meeting point of three different areas of research, namely: signal analysis, quantization and pseudo-differential operators. We extend then the correspondence between symbol and operator which characterizes localization operators to a more general situation, introducing the class of bilocalization operators. We show that this enlargement yields
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Mass concentration phenomenon in the 3D bipolar compressible Navier–Stokes–Poisson system J. Pseudo-Differ. Oper. Appl. (IF 1.1) Pub Date : 2024-02-10
Abstract In this paper, we investigate the blow-up mechanism to the bipolar compressible Navier–Stokes–Poisson system in three dimensions. It is essentially shown that the mass of the model will concentrate in some spatial points, even if the initial density contains vacuum states, provided that the smooth solution develops singularity in finite time.
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A new approach to neural networks using pseudo-differential operators J. Pseudo-Differ. Oper. Appl. (IF 1.1) Pub Date : 2024-01-21 Hang Du, Shahla Molahajloo, Xiaogang Wang
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Optimal semiclassical spectral asymptotics for differential operators with non-smooth coefficients J. Pseudo-Differ. Oper. Appl. (IF 1.1) Pub Date : 2024-01-16 Søren Mikkelsen
We consider differential operators defined as Friedrichs extensions of quadratic forms with non-smooth coefficients. We prove a two-term optimal asymptotic for the Riesz means of these operators and thereby also reprove an optimal Weyl law under certain regularity conditions. The methods used are then extended to consider more general admissible operators perturbed by a rough differential operator
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Boundedness of multilinear pseudo-differential operators with $$S_{0,0}$$ class symbols on Besov spaces J. Pseudo-Differ. Oper. Appl. (IF 1.1) Pub Date : 2024-01-16 Naoto Shida
We consider multilinear pseudo-differential operators with symbols in the multilinear Hörmander class \(S_{0, 0}\). The aim of this paper is to discuss the boundedness of these operators in the settings of Besov spaces.
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Weak solvability and well-posedness of some fractional parabolic problems with vanishing initial datum J. Pseudo-Differ. Oper. Appl. (IF 1.1) Pub Date : 2024-01-03 Abderrahim Charkaoui
This paper tackles a class of nonlinear parabolic equations driven by the fractional p-Laplacian operator with a vanishing initial datum. Our primary aim is to investigate the well-posedness (existence and uniqueness) of solutions to the proposed model. Notably, we will establish two interesting results concerning the existence and uniqueness of weak solutions. The first result pertains to the scenario
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Further investigation of stochastic nonlinear Hilfer-fractional integro-differential inclusions using almost sectorial operators J. Pseudo-Differ. Oper. Appl. (IF 1.1) Pub Date : 2023-12-12 Hasanen A. Hammad, Hassen Aydi, Doha A. Kattan
The purpose of this work is to develop a new model of fractional operators called Hilfer-fractional random nonlinear integro-differential equations. In this paradigm, a further discussion is encouraged under almost sectorial operators. The results are supported by fractional calculus, stochastic analysis theory, and Bohnenblust–Karlin’s fixed point theorem for multi-valued mappings. In addition, a
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On single-layer potentials, pseudo-gradients and a jump theorem for an isotropic $$\alpha $$ -stable stochastic process J. Pseudo-Differ. Oper. Appl. (IF 1.1) Pub Date : 2023-12-08 Khrystyna Mamalyha, Mykhailo Osypchuk
The aim of this paper is a behavior investigation of pseudo-gradients with respect to the spatial variable of a single-layer potential if the spatial point tends to some point in the carrier surface of the potential. The potentials connect to the generator of an isotropic \(\alpha \)-stable stochastic process with the power \(\alpha \in (1,2]\). This generator is the fractional Laplacian of the order
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Controlled continuous $$*$$ -g-frames in Hilbert $$C^{*}$$ -modules J. Pseudo-Differ. Oper. Appl. (IF 1.1) Pub Date : 2023-12-08 M’hamed Ghiati, Mohamed Rossafi, Mohammed Mouniane, Hatim Labrigui, Abdeslam Touri
The frame theory is a dynamic and exciting field with various applications in pure and applied mathematics. In this paper, we introduce and study the concept of controlled continuous \(*\)-g-frames in Hilbert \(C^{*}\)-modules, which is a generalization of discrete controlled \(*\)-g-frames in Hilbert \(C^{*}\)-modules. Additionally, we present some properties.
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Generalised Hardy type and Rellich type inequalities on the Heisenberg group J. Pseudo-Differ. Oper. Appl. (IF 1.1) Pub Date : 2023-12-08 Abimbola Abolarinwa, Michael Ruzhansky
This paper is primarily devoted to a class of interpolation inequalities of Hardy and Rellich types on the Heisenberg group \(\mathbb {H}^n\). Consequently, several weighted Hardy type, Heisenberg–Pauli–Weyl uncertainty principle and Hardy–Rellich type inqualities are established on \(\mathbb {H}^n\). Moreover, new weighted Sobolev type embeddings are derived. Finally, an integral inequality for vector
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On $$L^2$$ boundedness of rough Fourier integral operators J. Pseudo-Differ. Oper. Appl. (IF 1.1) Pub Date : 2023-12-08 Guoning Wu, Jie Yang
In this paper, let \(T_{a,\varphi }\) be a Fourier integral operator with rough amplitude \(a \in {L^\infty }S_\rho ^m\) and rough phase \(\varphi \in {L^\infty }{\Phi ^2}\) which satisfies a new class of rough non-degeneracy condition. When \(0 \leqslant \rho \leqslant 1\), if \(m < \frac{{n(\rho - 1)}}{2} - \frac{{\rho (n - 1)}}{4}\), we obtain that \(T_{a,\varphi }\) is bounded on \({L^2}\). Our
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Modified version of fixed point theorems and their applications on a fractional hybrid differential equation in the space of continuous tempered functions J. Pseudo-Differ. Oper. Appl. (IF 1.1) Pub Date : 2023-11-27 Sudip Deb, Anupam Das
This article contains modified version of fixed point theorems with the help of freshly made contraction operators and the solvability of a fractional hybrid differential equation involving Caputo fractional derivative by using modified Darbo’s fixed point theorem in the space of continuous tempered functions. The fundamental tool used in the solvability of the fractional hybrid differential equation
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Long time behavior of solutions for time-fractional pseudo-parabolic equations involving time-varying delays and superlinear nonlinearities J. Pseudo-Differ. Oper. Appl. (IF 1.1) Pub Date : 2023-11-09 Do Lan, Tran Van Tuan
We study the long time behavior of solutions for time-fractional pseudo-parabolic equations involving time-varying delays and nonlinear pertubations, where the nonlinear term is allowed to have superlinear growth. Concerning the associated linear problem, we establish a variation-of-parameters formula of mild solutions and prove some regularity estimates of resolvent operators. In addition, thanks
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Weighted norm inequalities related to fractional Schrödinger operators J. Pseudo-Differ. Oper. Appl. (IF 1.1) Pub Date : 2023-11-06 Zhiyong Wang, Pengtao Li, Yu Liu
Let \(L=-\Delta +V\) be a Schrödinger operator on \(\mathbb {R}^{n}\) with \(n\ge 3\), where the nonnegative potential V satisfies a reverse Hölder inequality. This paper is devoted to investigating the bounded behaviors of the semigroup maximal operators and fractional square functions related to the Schrödinger operator and their corresponding commutators on the weighted Morrey spaces containing
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Representations of frames via iterative actions of operators in tensor product spaces J. Pseudo-Differ. Oper. Appl. (IF 1.1) Pub Date : 2023-11-01 Nabin Kumar Sahu, Shalini Chauhan, Ram N. Mohapatra
The purpose of this paper is to study the dynamical representation of frames in tensor product of two Hilbert spaces \(H_1 \otimes H_2\). We have considered frames in \(H_1 \otimes H_2\) and established that they have dynamical representations and can be generated by some frame elements. In addition, we determined their canonical dual frames and showed that the canonical dual frames have also iterative
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Sharp Pitt’s inequality and Beckner’s logarithmic uncertainty principle for the Weinstein transform J. Pseudo-Differ. Oper. Appl. (IF 1.1) Pub Date : 2023-10-28 Minggang Fei, Jiali Zhou
In this paper, we prove the sharp Pitt’s inequality for the Weinstein transform. As an application, the Beckner’s logarithmic uncertainty principle for the Weinstein transform is established.
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Frame multiresolution analysis on $${\mathbb {Q}}_p$$ J. Pseudo-Differ. Oper. Appl. (IF 1.1) Pub Date : 2023-10-24 Debasis Haldar, Animesh Bhandari
Multiresolution analysis is a mathematical tool used to decompose functions in different resolution subspaces, where the scaling function plays a key role to construct the nested subspaces in \(L^{2}({\mathbb {R}})\). This paper presents a generalization of the same in \(L^{2}({\mathbb {Q}}_p)\), called frame multiresolution analysis (FMRA). So FMRA is a generalization of multiresolution analysis with
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Truncation quantization in the edge calculus J. Pseudo-Differ. Oper. Appl. (IF 1.1) Pub Date : 2023-10-24 B.-Wolfgang Schulze, Jörg Seiler
Pseudodifferential operators on the half-space associated with classical symbols of order zero without transmission property are shown to belong to the so-called edge algebra.
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Statistical de Rham Hodge operators and general Kastler-Kalau-Walze type theorems for manifolds with boundary J. Pseudo-Differ. Oper. Appl. (IF 1.1) Pub Date : 2023-10-16 Hongfeng Li, Tong Wu, Yong Wang
In this paper, we establish some general Kastler-Kalau-Walze type theorems for any dimensional manifolds with boundary which generalize the results in (Wei and Wang, J Nonlinear Math Phys 28: 254–275, 2021).
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Localization operators related to Stockwell transforms on locally compact abelian groups J. Pseudo-Differ. Oper. Appl. (IF 1.1) Pub Date : 2023-10-16 Fatemeh Esmaeelzadeh
In the present paper, we consider a locally compact abelian (L.C.A) group G and a topological automorphism \(\alpha \) on G. Associated to the topological automorphism \(\alpha \) on G, we introduce the Stockwell transform \(S_{\varphi , \alpha }\), where \(\varphi \in {L^2(G)}\). Then we show that the range of the Stockwell transform \(S_{\varphi , \alpha }\) is reproducing kernel Hilbert space. Moreover
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On the boundedness of rough bi-parameter Fourier integral operators J. Pseudo-Differ. Oper. Appl. (IF 1.1) Pub Date : 2023-10-14 Guangqing Wang, Jinhui Li
Let the bi-parameter Fourier integral operators be defined by the phase functions \(\varphi _{1}(x_{1},\xi ),\varphi _{2}(x_{2},\xi )\in L^\infty \Phi ^2\) satisfying the rough non-degeneracy condition and the amplitude \(a\in L^{p}BS^{m}_{\varrho }\) with \(m=(m_{1},m_{2})\in {\mathbb {R}}^{2}\), \(\varrho =(\varrho _{1},\varrho _{2})\in [0,1]\times [0,1]\). It is proved that if \(0
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New classes of parabolic pseudo-differential equations, Feller semigroups, contraction semigroups and stochastic process on the p-adic numbers J. Pseudo-Differ. Oper. Appl. (IF 1.1) Pub Date : 2023-10-06 Anselmo Torresblanca-Badillo, Alfredo R. R. Narváez, José López-González
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Decay rate of the solutions to the Cauchy problem of the Lord Shulman thermoelastic Timoshenko model with microtemperature effect J. Pseudo-Differ. Oper. Appl. (IF 1.1) Pub Date : 2023-10-09 Abdelbaki Choucha, Sofian Abuelbacher Adam Saad, Rashid Jan, Salah Boulaaras
In this work, we deal with a one-dimensional Cauchy problem in Timoshenko system with temperature and microtemperature effect. The heat conduction is given by the theory of Lord–Shulman. We prove that the dissipation induced by the coupling of the Timoshenko system with the heat conduction of Lord–Shulman’s theory alone is strong enough to stabilize the system, but with slow decay rate. To show our
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Semilinear degenerate elliptic equation in the presence of singular nonlinearity J. Pseudo-Differ. Oper. Appl. (IF 1.1) Pub Date : 2023-10-06 Kaushik Bal, Sanjit Biswas
Given \(\Omega (\subseteq \mathbb {R}^{1+m})\), a smooth bounded domain and a nonnegative measurable function f defined on \(\Omega \) with suitable summability. In this paper, we will study the existence and regularity of solutions to the quasilinear degenerate elliptic equation with a singular nonlinearity given by: $$\begin{aligned} -\Delta _\lambda u&=\frac{f}{u^{\nu }} \text { in }\Omega \\&u>0
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Boundary value problem with tempered fractional derivatives and oscillating term J. Pseudo-Differ. Oper. Appl. (IF 1.1) Pub Date : 2023-09-30 César E. Torres Ledesma, Hernán Cuti, Jesús Ávalos Rodríguez, Manuel Montalvo Bonilla
In this article, a class of boundary value problem with tempered fractional derivatives is studied. By using a variational principle due to Ricceri (in J Comput Appl Math 113:401–410, 2000), the existence of infinitely many weak solutions for these problems is established by requiring that the nonlinear term f has a suitable oscillating behavior either at the origin or at infinity.
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Study of a sequential $$\psi $$ -Hilfer fractional integro-differential equations with nonlocal BCs J. Pseudo-Differ. Oper. Appl. (IF 1.1) Pub Date : 2023-09-15 Faouzi Haddouchi, Mohammad Esmael Samei, Shahram Rezapour
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Estimates for the first eigenvalue of diffusion-type operators in weighted manifolds J. Pseudo-Differ. Oper. Appl. (IF 1.1) Pub Date : 2023-09-15 Pengyan Wang, Fanqi Zeng
We provide several lower bounds for the first eigenvalue for some classical eigenvalue problems with respect to the diffusion-type operator \({\mathbb {L}}_{\phi , V}\) in weighted manifolds with boundary and under some conditions on the weighted Ricci curvature \(\widehat{Ric}_{\phi ,m}^{V}\) and \(\phi \)-mean curvature \(H_{\phi }\). A key tool in the proof is the generalized Reilly formula in weighted
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Bilinear multipliers on Orlicz spaces on locally compact groups J. Pseudo-Differ. Oper. Appl. (IF 1.1) Pub Date : 2023-09-09 Alen Osançlıol, Serap Öztop
We generalize the theory of bilinear multipliers acting on Orlicz spaces from \(\mathbb {R}^n\) to locally compact abelian groups. We focus on describing these bilinear multipliers from the point of view of abstract harmonic analysis. We obtain separate necessary and sufficient conditions for the existence and boundedness of such bilinear multipliers.
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Fractional Fourier transform for space–time algebra-valued functions J. Pseudo-Differ. Oper. Appl. (IF 1.1) Pub Date : 2023-09-04 Mohra Zayed, Youssef El Haoui
The aim of this article is to introduce a fractional space–time Fourier transform (FrSFT) by generalizing the fractional Fourier transform for 16-dimensional space–time \(C \hspace{-1.00006pt}\ell _{3,1}\)-valued signals over the domain of space–time (Minkowski space) \(\mathbb {R}^{3, 1}\). The primary analysis includes the investigation of fundamental properties such as the inversion, the Plancherel
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Solvability of an infinite system of fractional differential equations with p-Laplacian operator in a new tempered sequence space J. Pseudo-Differ. Oper. Appl. (IF 1.1) Pub Date : 2023-09-04 Mohammad Mursaleen, Ekrem Savaş
In this article, an infinite system of three point boundary value problem of p-Laplacian operator is considered for the existence of solution in a new sequence space related to the tempered sequence space \(\ell _{p}^{\alpha },\) \(p\ge 1\), via the technique of the Hausdorff measure of noncompactness. To illustrate our new results in tempered sequence spaces, we provide a numerical example.
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Two disjoint and infinite sets of solutions for a nonlocal problem involving a Hardy potential and critical growth with concave nonlinearities J. Pseudo-Differ. Oper. Appl. (IF 1.1) Pub Date : 2023-08-21 Rachid Echarghaoui, Moussa Khouakhi, Mohamed Masmodi
In this paper, we consider the following problem involving fractional Laplacian with a Hardy potential operator $$\begin{aligned} \left\{ \begin{array}{ll} (-\Delta )^{\alpha } u -\mu \dfrac{u}{\vert x\vert ^{2\alpha }}=\vert u\vert ^{2_{\alpha }^{*}-2} u+\lambda \vert u\vert ^{q-2}u, &{} \text{ in } \Omega , \\ u=0, &{} \text{ on } \partial \Omega , \end{array}\right. \end{aligned}$$ where \(\Omega
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A weighted $$L_p$$ -regularity theory for parabolic partial differential equations with time-measurable pseudo-differential operators J. Pseudo-Differ. Oper. Appl. (IF 1.1) Pub Date : 2023-08-21 Jae-Hwan Choi, Ildoo Kim
We obtain the existence, uniqueness, and regularity estimates of the following Cauchy problem $$\begin{aligned} {\left\{ \begin{array}{ll} \partial _tu(t,x)=\psi (t,-i\nabla )u(t,x)+f(t,x), &{} \quad (t,x)\in (0,T)\times {\mathbb {R}}^d,\\ u(0,x)=0, &{} \quad x\in {\mathbb {R}}^d, \end{array}\right. } \end{aligned}$$(0.1) in (Muckenhoupt) weighted \(L_p\)-spaces with time-measurable pseudo-differential
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Uncertainty principles for the fractional quaternion fourier transform J. Pseudo-Differ. Oper. Appl. (IF 1.1) Pub Date : 2023-08-21 Fatima Elgadiri, Abdellatif Akhlidj
The Fractional Quaternion Fourier transform (FrQFT) is a generalization of the usual Quaternion Fourier Transform \({\mathcal {F}}_Q\). The aim of this paper is to prove some qualitative and quantitative uncertainty principles for FrQFT. The first result consists the Hardy’s and an \(L^p-L^q\)-version of Miyachi’s theorems for the FrQFT, which estimates the decay of two fractional quaternion Fourier
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Localization operators and wavelet multipliers involving two-dimensional linear canonical curvelet transform J. Pseudo-Differ. Oper. Appl. (IF 1.1) Pub Date : 2023-07-25 Viorel Catană, Mihaela-Graţiela Scumpu
The main purpose of this paper is to introduce and study the localization operators and the wavelet multipliers associated to two-dimensional linear canonical curvelet transform. We investigate the \(L^{2}\)-boundedness, compactness and Schatten-von Neumann properties for these classes of operators.
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On g-frame representations via linear operators J. Pseudo-Differ. Oper. Appl. (IF 1.1) Pub Date : 2023-07-17 S. Jahedi, F. Javadi, M. J. Mehdipour
Let \(\{\mathfrak {M} _k \} _{ k \in {\mathbb {Z}}} \) be a sequence of closed subspaces of Hilbert space H, and let \(\{\Theta _k\}_{k \in {\mathbb {Z}}}\) be a sequence of linear operators from H into \(\mathfrak {M}_k\), \(k \in {\mathbb {Z}}\). In the case where, \(\Theta _k\) is self-adjoint and \(\Theta _k(\mathfrak {M} _k)= \mathfrak {M} _k\) for all \(k \in {\mathbb {Z}}\), we show that if
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Symmetrically global pseudo-differential operators involving the Weinstein transform J. Pseudo-Differ. Oper. Appl. (IF 1.1) Pub Date : 2023-07-14 Mohd Sartaj, S. K. Upadhyay
In this paper, boundedness and compactness results for symmetrically global pseudo-differential operator on \(L^{p}_{\alpha }({\mathbb {R}}^{n+1}_{+})\)-type Sobolev space \( {\mathcal {H}}^{r,s,p}_{\alpha } \) of order (r, s) are investigated by exploiting the theory of the Weinstein transform. Using symmetrically global symbol \( \sigma (x,\xi )\) in \( S^{m_{1}, m_{2}}, ~m_{1}, m_{2} \in {\mathbb
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$$\Theta $$ -type Calderón–Zygmund operator and its commutator on (grand) generalized weighted variable exponent Morrey space over RD-spaces J. Pseudo-Differ. Oper. Appl. (IF 1.1) Pub Date : 2023-07-09 Guanghui Lu, Shuangping Tao, Ronghui Liu
Let \((\mathcal {X},d,\mu )\) be a RD-space satisfying both the doubling and reverse doubling conditions. In this setting, the authors first obtain the definitions of a generalized weighted variable exponent Morrey space \(\mathcal {L}^{p(\cdot ),\varphi }_{\omega }(\mathcal {X})\) and a grand generalized weighted variable exponent Morrey space \(\mathcal {L}^{p(\cdot ),\varphi ,\alpha }_{\omega }(\mathcal
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Special Fourier integral operators of types I and II with function-variable symbols: definition, relation to metaplectic transform, and Heisenberg’s uncertainty principles J. Pseudo-Differ. Oper. Appl. (IF 1.1) Pub Date : 2023-07-07 Ga Wang, Zhichao Zhang
This study devotes to Heisenberg’s uncertainty principles for Fourier integral operators of types I and II with function-variable symbols, i.e., the symbol \(\sigma \in S_{1\otimes v_s}^{\infty }(\mathbb {R}^N)\) of the type I Fourier integral operator is only \(\textbf{w}\)-dependent and the symbol \(\tau \in S_{1\otimes v_s}^{\infty }(\mathbb {R}^N)\) of the type II Fourier integral operator is only
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Dual Boas-type theorems and weighted integrability results for second Hankel–Clifford transform J. Pseudo-Differ. Oper. Appl. (IF 1.1) Pub Date : 2023-06-26 Sergey Volosivets
For a measurable on \({\mathbb {R}}_+\) function from \(L^p\) space with a power weight \(x^\mu \) we consider the Hankel–Clifford transform \(h_{2,\mu }(f)\). We proved a dual Boas type result about necessary and sufficient conditions for \(h_{2,\mu }(f)\) to belong to the generalized uniform Lipschitz classes connected with the Hankel–Clifford translation. We obtain sufficient conditions for the
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On evolution of the classical heat and the quantum wave generated by the Laplacian on the Heisenberg group J. Pseudo-Differ. Oper. Appl. (IF 1.1) Pub Date : 2023-06-23 M. W. Wong, Shengwen Yang
The Laplacian on the Heisenberg group as a sum of squares of the standard vector fields on the Heisenberg group is first made explicit to be a Laplace–Beltrami operator on the Heisenberg group, which is well known to be a Riemannian manifold. The dissipation of the heat generated by the Laplacian on the Heisenberg group is then given in terms of estimates reminiscent of the Hausdorff–Young inequalities
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Average sampling and reconstruction of quasi shift-invariant stochastic processes J. Pseudo-Differ. Oper. Appl. (IF 1.1) Pub Date : 2023-06-21 Yingchun Jiang, Haiying Zhang
In this paper, we mainly study the average sampling and reconstruction of quasi shift-invariant stochastic processes, which can include more random signal models than classical shift-invariant spaces. First, we establish two average sampling theorems in the sense of mean-square convergence. Then, we estimate the truncation errors for the corresponding two kinds of average sampling schemes.
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Pseudodifferential operators with completely periodic symbols J. Pseudo-Differ. Oper. Appl. (IF 1.1) Pub Date : 2023-06-17 Gianluca Garello, Alessandro Morando
Motivated by the recent paper of Boggiatto–Garello (J Pseudo-Differ Oper Appl 11:93–117, 2020) where a Gabor operator is regarded as pseudodifferential operator with symbol \(p(x,\omega )\) periodic on both the variables, we study the continuity and invertibility, on general time frequency invariant spaces, of pseudodifferential operators with completely periodic symbol and general \(\tau \) quantization
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Boundedness for Littlewood-Paley functions on weighted Morrey-type spaces related to certain nonnegative potentials J. Pseudo-Differ. Oper. Appl. (IF 1.1) Pub Date : 2023-06-19 Nan Zhao, Jiang Zhou, Yu Liu
Let \(L:=-\Delta +V\) be the Schrödinger operator on \({\mathbb {R}}^{n}\) with \(n\ge 3\), where V is a nonnegative potential belonging to certain reverse Hölder class \(RH_{q}({\mathbb {R}}^{n})\) with \(q>n/2\). Applying a new class of weights \(A_{p}^{\rho }\) which is larger than the classical Muckenhoupt’s weights, we obtain the boundedness on weighted Morrey-type spaces for Littlewood-Paley
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Large time asymptotics for the fractional modified Korteweg-de Vries equation of order $$\alpha \in \left[ 4,5\right) $$ J. Pseudo-Differ. Oper. Appl. (IF 1.1) Pub Date : 2023-06-09 Rafael Carreño-Bolaños, Pavel I. Naumkin
We study the large time asymptotics of solutions to the Cauchy problem for the fractional modified Korteweg-de Vries equation $$\begin{aligned} \left\{ \begin{array}{l} \partial _{t}w+\frac{1}{\alpha }\left| \partial _{x}\right| ^{\alpha -1}\partial _{x}w=\partial _{x}\left( w^{3}\right) ,\text { }t>0,\, x\in {\mathbb {R}}\textbf{,}\\ w\left( 0,x\right) =w_{0}\left( x\right) ,\,x\in {\mathbb {R}} \textbf{
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Investigation of fractional order inclusion problem with Mittag-Leffler type derivative J. Pseudo-Differ. Oper. Appl. (IF 1.1) Pub Date : 2023-06-09 Adel Lachouri, Mohammed S. Abdo, Abdelouaheb Ardjouni, Kamal Shah, Thabet Abdeljawad
Inclusions problems due to differential equations arise in many situations like variational inequalities, projective dynamical systems, and many more. Therefore, the said area has given proper attentions in the last many years. The mentioned area has been extended to fractional order problems recently. The inclusion problems under the usual Caputo and Reimann-Liouville derivatives have been studied
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Morse’s theory and local linking for a fractional $$(p_{1}(\textrm{x}.,), p_{2}(\textrm{x}.,))$$ : Laplacian problems on compact manifolds J. Pseudo-Differ. Oper. Appl. (IF 1.1) Pub Date : 2023-06-07 Ahmed Aberqi, Abdesslam Ouaziz
In this paper, we compute critical groups for establishing the existence of solutions for the following fractional \(\displaystyle (p_{1}(\textrm{x},.), p_{2}(\textrm{x},.))\)—Laplacian problem involving a singular term: $$\begin{aligned} \begin{aligned} \left\{ \begin{array}{llll} (\mathcal {L}_{\textrm{g}} ^{s_{1}})_{p_{1}(\textrm{x},.)} \textrm{u}(\textrm{x})+ (\mathcal {L}_{\textrm{g}} ^{s_{2}
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Nuclearity for power series kernels in higher dimensions J. Pseudo-Differ. Oper. Appl. (IF 1.1) Pub Date : 2023-06-01 Julio Delgado, Liliana Posada
In this work we establish the nuclearity on Lebesgue spaces for a class of power series kernels in higher dimensions. This class includes important examples arising as Maclaurin series kernels as well as the Fox-Li and related operators. As a consequence we derive the rate of decay of the corresponding eigenvalues and trace formulae.