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A Restriction Estimate with a Log-Concavity Assumption J. Fourier Anal. Appl. (IF 1.2) Pub Date : 2024-03-14 Kyoungtae Moon
The purpose of this paper is to prove an optimal restriction estimate for a class of flat curves in \({\mathbb {R}} ^d\), \(d\ge 3\). Namely, we consider the problem of determining all the pairs (p, q) for which the \(L^p-L^q\) estimate holds (or a suitable Lorentz norm substitute at the endpoint, where the \(L^p-L^q\) estimate fails) for the extension operator associated to \(\gamma (t) = (t, {\frac{t^2}{2
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One-Dimensional Discrete Hardy and Rellich Inequalities on Integers J. Fourier Anal. Appl. (IF 1.2) Pub Date : 2024-03-08 Shubham Gupta
In this paper, we consider a weighted version of one-dimensional discrete Hardy inequalities with power weights of the form \(n^\alpha \). We prove the inequality when \(\alpha \) is an even natural number with the sharp constant and remainder terms. We also find explicit constants in standard and weighted Rellich inequalities(with weights \(n^\alpha \)) which are asymptotically sharp as \(\alpha \rightarrow
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Shape Holomorphy of Boundary Integral Operators on Multiple Open Arcs J. Fourier Anal. Appl. (IF 1.2) Pub Date : 2024-02-27 José Pinto, Fernando Henríquez, Carlos Jerez-Hanckes
We establish shape holomorphy results for general weakly- and hyper-singular boundary integral operators arising from second-order partial differential equations in unbounded two-dimensional domains with multiple finite-length open arcs. After recasting the corresponding boundary value problems as boundary integral equations, we prove that their solutions depend holomorphically upon perturbations of
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Cosine Sign Correlation J. Fourier Anal. Appl. (IF 1.2) Pub Date : 2024-02-08 Shilin Dou, Ansel Goh, Kevin Liu, Madeline Legate, Gavin Pettigrew
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Stable Separation of Orbits for Finite Abelian Group Actions J. Fourier Anal. Appl. (IF 1.2) Pub Date : 2024-02-05 Jameson Cahill, Andres Contreras, Andres Contreras Hip
In this paper we construct two new families of invariant maps that separate the orbits of the action of a finite Abelian group on a finite dimensional complex vector space. One of these families is Lipschitz continuous with respect to the quotient metric on the space of orbits, but involves computing large powers of the components of the vectors which can lead to instabilities. The other family avoids
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The Turán Problem and Its Dual for Positive Definite Functions Supported on a Ball in $${\mathbb {R}}^d$$ J. Fourier Anal. Appl. (IF 1.2) Pub Date : 2024-02-05 Jean-Pierre Gabardo
The Turán problem for an open ball of radius r centered at the origin in \({\mathbb {R}}^d\) consists in computing the supremum of the integrals of positive definite functions compactly supported on that ball and taking the value 1 at the origin. Siegel proved, in the 1930s that this supremum is equal to \(2^{-d}\) mutiplied by the Lebesgue measure of the ball and is reached by a multiple of the self-convolution
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A Class of Oscillatory Singular Integrals with Rough Kernels and Fewnomials Phases J. Fourier Anal. Appl. (IF 1.2) Pub Date : 2024-01-10 Jiao Ma, Chenyan Wang, Huoxiong Wu
This paper is concerned with the oscillatory singular integral operator \(T_Q\) defined by $$\begin{aligned} T_Qf(x)=\mathrm{p.v.}\int _{{\mathbb {R}^n}}f(x-y)\frac{\Omega (y)}{|y|^n}e^{iQ(|y|)}dy, \end{aligned}$$ where \(Q(t)=\sum _{1\le i\le m}a_it^{\alpha _i}\) is a real-valued polynomial on \(\mathbb {R}\), \(\Omega \) is a homogenous function of degree zero on \(\mathbb {R}^n\) with mean value
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The Schatten Classes of Calderón–Zygmund Operators J. Fourier Anal. Appl. (IF 1.2) Pub Date : 2024-01-10 Paco Villarroya
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A Family of Fractal Fourier Restriction Estimates with Implications on the Kakeya Problem J. Fourier Anal. Appl. (IF 1.2) Pub Date : 2024-01-10 Bassam Shayya
In a recent paper, Du and Zhang (Ann Math 189:837–861, 2019) proved a fractal Fourier restriction estimate and used it to establish the sharp \(L^2\) estimate on the Schrödinger maximal function in \(\mathbb R^n\), \(n \ge 2\). In this paper, we show that the Du–Zhang estimate is the endpoint of a family of fractal restriction estimates such that each member of the family (other than the original)
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Limited Range Extrapolation with Quantitative Bounds and Applications J. Fourier Anal. Appl. (IF 1.2) Pub Date : 2024-01-10 Mingming Cao, Honghai Liu, Zengyan Si, Kôzô Yabuta
In recent years, sharp or quantitative weighted inequalities have attracted considerable attention on account of the \(A_2\) conjecture solved by Hytönen. Advances have greatly improved conceptual understanding of classical objects such as Calderón–Zygmund operators. However, plenty of operators do not fit into the class of Calderón–Zygmund operators and fail to be bounded on all \(L^p(w)\) spaces
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Modified Ambiguity Function and Wigner Distribution Associated With Quadratic-Phase Fourier Transform J. Fourier Anal. Appl. (IF 1.2) Pub Date : 2024-01-04 Tien Minh Lai
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Separating Fourier and Schur Multipliers J. Fourier Anal. Appl. (IF 1.2) Pub Date : 2024-01-02 Cédric Arhancet, Christoph Kriegler, Christian Le Merdy, Safoura Zadeh
Let G be a locally compact unimodular group, let \(1\le p<\infty \), let \(\phi \in L^\infty (G)\) and assume that the Fourier multiplier \(M_\phi \) associated with \(\phi \) is bounded on the noncommutative \(L^p\)-space \(L^p(VN(G))\). Then \(M_\phi L^p(VN(G))\rightarrow L^p(VN(G))\) is separating (that is, \(\{a^*b=ab^*=0\}\Rightarrow \{M_\phi (a)^* M_\phi (b)=M_\phi (a)M_\phi (b)^*=0\}\) for any
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$$L^2$$ Estimates for a Nikodym Maximal Function Associated to Space Curves J. Fourier Anal. Appl. (IF 1.2) Pub Date : 2024-01-02 Aswin Govindan Sheri
For \(p \in [2,\infty )\), we consider the \(L^p \rightarrow L^p\) boundedness of a Nikodym maximal function associated to a one-parameter family of tubes in \({\mathbb {R}}^{d+1}\) whose directions are determined by a non-degenerate curve \(\gamma \) in \({\mathbb {R}}^d\). These operators arise in the analysis of maximal averages over space curves. The main theorem generalises the known results for
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On Ultradifferentiable Regularity of Perturbations by Lower Order Terms of Globally $$C^\infty$$ Hypoelliptic Ultradifferentiable Pseudodifferential Operators J. Fourier Anal. Appl. (IF 1.2) Pub Date : 2023-12-29 Igor Ambo Ferra, Gerson Petronilho
We prove \({\mathcal {M}}\)-regularity for a class of pseudodifferential operators in ultradifferentiable classes defined on the torus \(\mathbb {T}^{m+n}\) which are globally \(C^{\infty }\) hypoelliptic. The same property is also valid for certain perturbations of these operators by lower order terms.
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Trigonometric Polynomials with Frequencies in the Set of Squares and Divisors in a Short Interval J. Fourier Anal. Appl. (IF 1.2) Pub Date : 2023-12-19 Mikhail R. Gabdullin
Let \(\gamma _0=\frac{\sqrt{5}-1}{2}=0.618\ldots \). We prove that, for any \(\varepsilon >0\) and any trigonometric polynomial f with frequencies in the set \(\{n^2: N \leqslant n\leqslant N+N^{\gamma _0-\varepsilon }\}\), the inequality $$\begin{aligned} \Vert f\Vert _4 \ll \varepsilon ^{-1/4}\Vert f\Vert _2 \end{aligned}$$ holds, which makes a progress on a conjecture of Cilleruelo and Córdoba.
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Sharp Hardy’s Inequality for Orthogonal Expansions in $$H^p$$ Spaces J. Fourier Anal. Appl. (IF 1.2) Pub Date : 2023-12-19 Paweł Plewa
Hardy’s inequality on \(H^p\) spaces, \(p\in (0,1]\), in the context of orthogonal expansions is investigated for general bases on a wide class of domains in \(\mathbb {R}^d\) with Lebesgue measure. The obtained result is applied to various Hermite, Laguerre, and Jacobi expansions. For that purpose some delicate estimates of the higher order derivatives for the underlying functions and of the associated
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Uniform Resolvent Estimates for Laplace–Beltrami Operator on the Flat Euclidean Cone J. Fourier Anal. Appl. (IF 1.2) Pub Date : 2023-12-01 Jialu Wang, Chengbin Xu
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Components and Exit Times of Brownian Motion in Two or More p-Adic Dimensions J. Fourier Anal. Appl. (IF 1.2) Pub Date : 2023-11-20 Rahul Rajkumar, David Weisbart
The fundamental solution to a pseudo-differential equation for functions defined on the d-fold product of the p-adic numbers, \(\mathbb {Q}_p\), induces an analogue of the Wiener process in \(\mathbb {Q}_p^d\). As in the real setting, the components are 1-dimensional p-adic Brownian motions with the same diffusion constant and exponent as the original process. Asymptotic analysis of the conditional
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A Note on the Operator Window of Modulation Spaces J. Fourier Anal. Appl. (IF 1.2) Pub Date : 2023-11-20 Weichao Guo, Guoping Zhao
Inspired by the recent article Skrettingland (J. Fourier Anal. Appl. 28(2), 1–34 (2022)), this paper is devoted to the study of a suitable class of windows in the framework of bounded linear operators on \(L^2({{\mathbb {R}}}^{d})\). We establish a natural and complete characterization for the window class such that the corresponding STFT leads to equivalent norms on modulation spaces. The positive
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$$L^p$$ - $$L^q$$ Boundedness of Fourier Multipliers Associated with the Anharmonic Oscillator J. Fourier Anal. Appl. (IF 1.2) Pub Date : 2023-11-20 Marianna Chatzakou, Vishvesh Kumar
In this paper we study the \(L^p\)-\(L^q\) boundedness of the Fourier multipliers in the setting where the underlying Fourier analysis is introduced with respect to the eigenfunctions of an anharmonic oscillator A. Using the notion of a global symbol that arises from this analysis, we extend a version of the Hausdorff–Young–Paley inequality that guarantees the \(L^p\)-\(L^q\) boundedness of these operators
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Refinements of Berry–Esseen Inequalities in Terms of Lyapunov Coefficients J. Fourier Anal. Appl. (IF 1.2) Pub Date : 2023-11-16 Sergey G. Bobkov
We discuss some variants of the Berry–Esseen inequality in terms of Lyapunov coefficients which may provide sharp rates of normal approximation.
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Young’s Inequality for the Twisted Convolution J. Fourier Anal. Appl. (IF 1.2) Pub Date : 2023-11-01 P. K. Ratnakumar
We characterise the triples (p, q, r) for which the bi-linear \(\lambda \)-twisted convolution map \(B_\lambda : (f,g) \rightarrow f \times _\lambda \, g\) is bounded from \(L^p(\mathbb C^n) \times L^q(\mathbb C^n) \rightarrow L^r(\mathbb C^n)\) for \(1 \le p,q,r \le \infty \). This gives the analogue of Young’s inequality for the twisted convolution.
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Uncertainty Principle for Free Metaplectic Transformation J. Fourier Anal. Appl. (IF 1.2) Pub Date : 2023-11-01 Zhichao Zhang
This study devotes to Heisenberg’s uncertainty inequalities of complex-valued functions in two free metaplectic transformation (FMT) domains without the assumption of orthogonality. In our latest work (Zhang in J Fourier Anal Appl 27(4):68, 2021), it is crucial that the FMT needs to be orthogonal for a decoupling of the cross terms. Instead of applying the orthogonality assumption, our current work
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On Discrete Groups of Euclidean Isometries: Representation Theory, Harmonic Analysis and Splitting Properties J. Fourier Anal. Appl. (IF 1.2) Pub Date : 2023-11-01 Bernd Schmidt, Martin Steinbach
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A Note on the Jacobian Problem of Coifman, Lions, Meyer and Semmes J. Fourier Anal. Appl. (IF 1.2) Pub Date : 2023-10-20 Sauli Lindberg
Coifman, Lions, Meyer and Semmes asked in 1993 whether the Jacobian operator and other compensated compactness quantities map their natural domain of definition onto the real-variable Hardy space \(\mathcal {H}^1({\mathbb {R}}^n)\). We present an axiomatic, Banach space geometric approach to the problem in the case of quadratic operators. We also make progress on the main open case, the Jacobian equation
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Correction to: On Harmonic Hilbert Spaces on Compact Abelian Groups J. Fourier Anal. Appl. (IF 1.2) Pub Date : 2023-10-17 Suddhasattwa Das, Dimitrios Giannakis, Michael R. Montgomery
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The General Theory of Superoscillations and Supershifts in Several Variables J. Fourier Anal. Appl. (IF 1.2) Pub Date : 2023-10-17 F. Colombo, S. Pinton, I. Sabadini, D. C. Struppa
In this paper we describe a general method to generate superoscillatory functions of several variables starting from a superoscillating sequence of one variable. Our results are based on the study of suitable infinite order differential operators acting on holomorphic functions with growth conditions of exponential type. Additional constraints are required when dealing with infinite order differential
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On Eigenmeasures Under Fourier Transform J. Fourier Anal. Appl. (IF 1.2) Pub Date : 2023-10-11 Michael Baake, Timo Spindeler, Nicolae Strungaru
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Fractional Leibniz Rules in the Setting of Quasi-Banach Function Spaces J. Fourier Anal. Appl. (IF 1.2) Pub Date : 2023-10-11 Elizabeth Hale, Virginia Naibo
Fractional Leibniz rules are reminiscent of the product rule learned in calculus classes, offering estimates in the Lebesgue norm for fractional derivatives of a product of functions in terms of the Lebesgue norms of each function and its fractional derivatives. We prove such estimates for Coifman–Meyer multiplier operators in the setting of Triebel–Lizorkin and Besov spaces based on quasi-Banach function
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Bilinear Bochner–Riesz Square Function and Applications J. Fourier Anal. Appl. (IF 1.2) Pub Date : 2023-10-11 Surjeet Singh Choudhary, K. Jotsaroop, Saurabh Shrivastava, Kalachand Shuin
In this paper, we introduce Stein’s square function associated with bilinear Bochner–Riesz means and investigate its \(L^p-\)boundedness properties. Further, we discuss several applications of the square function in the context of bilinear multipliers. In particular, we obtain results for maximal function associated with generalised bilinear Bochner–Riesz means. This extends the results proved in [22]
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Heat Equations and Wavelets on Mumford Curves and Their Finite Quotients J. Fourier Anal. Appl. (IF 1.2) Pub Date : 2023-10-02 Patrick Erik Bradley
A class of heat operators over non-archimedean local fields acting on \(L_2\)-function spaces on holed discs in the local field are developed and seen as being operators previously introduced by Zúñiga-Galindo, and if the underlying trees are regular, they are associated here with certain finite Kronecker product graphs. \(L_2\)-spaces and integral operators invariant under the action of a finite group
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Refined Decay Estimate and Analyticity of Solutions to the Linear Heat Equation in Homogeneous Besov Spaces J. Fourier Anal. Appl. (IF 1.2) Pub Date : 2023-09-22 Tohru Ozawa, Taiki Takeuchi
The heat semigroup \(\{T(t)\}_{t \ge 0}\) defined on homogeneous Besov spaces \(\dot{B}_{p,q}^s(\mathbb {R}^n)\) is considered. We show the decay estimate of \(T(t)f \in \dot{B}_{p,1}^{s+\sigma }(\mathbb {R}^n)\) for \(f \in \dot{B}_{p,\infty }^s(\mathbb {R}^n)\) with an explicit bound depending only on the regularity index \(\sigma >0\) and space dimension n. It may be regarded as a refined result
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Two-Dimensional Hardy–Littlewood Theorem for Functions with General Monotone Fourier Coefficients J. Fourier Anal. Appl. (IF 1.2) Pub Date : 2023-09-19 Kristina Oganesyan
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Endpoint Entropy Fefferman–Stein Bounds for Commutators J. Fourier Anal. Appl. (IF 1.2) Pub Date : 2023-09-15 Pamela A. Muller, Israel P. Rivera-Ríos
In this paper endpoint entropy Fefferman–Stein bounds for Calderón–Zygmund operators introduced by Rahm (J Math Anal Appl 504(1):Paper No. 125372, 2021) are extended to iterated Coifman–Rochberg–Weiss commutators.
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Bernstein–Jackson Inequalities on Gaussian Hilbert Spaces J. Fourier Anal. Appl. (IF 1.2) Pub Date : 2023-09-12 Oleh Lopushansky
Estimates of best approximations by exponential type analytic functions in Gaussian random variables with respect to the Malliavin derivative in the form of Bernstein–Jackson inequalities with exact constants are established. Formulas for constants are expressed through basic parameters of approximation spaces. The relationship between approximation Gaussian Hilbert spaces and classic Besov spaces
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Riesz Transform Characterization of Hardy Spaces Associated with Ball Quasi-Banach Function Spaces J. Fourier Anal. Appl. (IF 1.2) Pub Date : 2023-08-21 Fan Wang, Dachun Yang, Wen Yuan
Let X be a ball quasi-Banach function space satisfying some mild assumptions and \(H_X(\mathbb {R}^n)\) the Hardy space associated with X. In this article, the authors introduce both the Hardy space \(H_X(\mathbb {R}^{n+1}_+)\) of harmonic functions and the Hardy space \(\mathbb {H}_X(\mathbb {R}^{n+1}_+)\) of harmonic vectors, associated with X, and then establish the isomorphisms among \(H_X(\mathbb
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The Lower Fourier Dimensions of In-Homogeneous Self-similar Measures J. Fourier Anal. Appl. (IF 1.2) Pub Date : 2023-08-18 Shuqin Zhang, Bing Gao, Yingqing Xiao
The in-homogeneous self-similar measure \(\mu \) is defined by the relation $$\begin{aligned} \mu =\sum _{j=1}^N p_j \mu \circ S_j^{-1}+p\nu , \end{aligned}$$ where \((p_1,\ldots ,p_N,p)\) is a probability vector, each \(S_j:\mathbb {R}^d\rightarrow \mathbb {R}^d\), \(j=1,\ldots ,N\), is a contraction similarity, and \(\nu \) is a Borel probability measure on \(\mathbb {R}^d\) with compact support
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Correction: Maximal Operator in Variable Stummel Spaces J. Fourier Anal. Appl. (IF 1.2) Pub Date : 2023-08-17 Alexandre Almeida, Humberto Rafeiro
In this note we fix some flaws in the proof of the main result on the boundedness of the maximal operator given in the paper mentioned in the title.
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Injectivity Conditions for STFT Phase Retrieval on $${\mathbb {Z}}$$ , $${\mathbb {Z}}_d$$ and $${{\mathbb {R}}}^d$$ J. Fourier Anal. Appl. (IF 1.2) Pub Date : 2023-08-08 David Bartusel
We study the phase retrieval problem for the short-time Fourier transform on the groups \({\mathbb {Z}}\), \({\mathbb {Z}}_d\) and \({{\mathbb {R}}}^d\). As is well-known, phase retrieval is possible once the windows’s ambiguity function vanishes nowhere. However, there are only few results for windows that fail to meet this condition. The goal of this paper is to establish new and complete characterizations
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Remarks on Dunkl Translations of Non-radial Kernels J. Fourier Anal. Appl. (IF 1.2) Pub Date : 2023-08-03 Jacek Dziubański, Agnieszka Hejna
On \( {\mathbb {R}}^N\) equipped with a root system R and a multiplicity function \(k>0\), we study the generalized (Dunkl) translations \(\tau _{{\textbf{x}}}g(-{\textbf{y}})\) of not necessarily radial kernels g. Under certain regularity assumptions on g, we derive bounds for \(\tau _{{\textbf{x}}}g(-{\textbf{y}})\) by means the Euclidean distance \(\Vert {\textbf{x}}-{\textbf{y}}\Vert \) and the
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Approximation of Nonlinear Functionals Using Deep ReLU Networks J. Fourier Anal. Appl. (IF 1.2) Pub Date : 2023-07-28 Linhao Song, Jun Fan, Di-Rong Chen, Ding-Xuan Zhou
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New Atomic Decomposition for Besov Type Space $$\dot{B}^0_{1,1}$$ Associated with Schrödinger Type Operators J. Fourier Anal. Appl. (IF 1.2) Pub Date : 2023-07-28 The Anh Bui, Xuan Thinh Duong
Let \((X, d, \mu )\) be a space of homogeneous type. Let L be a nonnegative self-adjoint operator on \(L^2(X)\) satisfying certain conditions on the heat kernel estimates which are motivated from the heat kernel of the Schrödinger operator on \(\mathbb {R}^n\). The main aim of this paper is to prove a new atomic decomposition for the Besov space \(\dot{B}^{0, L}_{1,1}(X)\) associated with the operator
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Fusion Frame Homotopy and Tightening Fusion Frames by Gradient Descent J. Fourier Anal. Appl. (IF 1.2) Pub Date : 2023-07-28 Tom Needham, Clayton Shonkwiler
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On the Weak Boundedness of Multilinear Littlewood–Paley Functions J. Fourier Anal. Appl. (IF 1.2) Pub Date : 2023-07-28 Mahdi Hormozi, Yoshihiro Sawano, Kôzô Yabuta
In this note, notwithstanding the generalization, we simplify and shorten the proofs of the main results of the third author’s paper (Shi et al in J Math Pures Appl 101:394–413, 2014) significantly. In particular, the new proof for Shi et al (J Math Pures Appl 101:394–413, 2014, Theorem 1.1) is quite short and, unlike the original proof, does not rely on the properties of the “Marcinkiewicz function”
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$$L_p$$ – $$L_q$$ Fourier Multipliers on Locally Compact Quantum Groups J. Fourier Anal. Appl. (IF 1.2) Pub Date : 2023-07-27 Haonan Zhang
Let \(\mathbb {G}\) be a locally compact quantum group with dual \(\widehat{\mathbb {G}}\). Suppose that the left Haar weight \(\varphi \) and the dual left Haar weight \(\widehat{\varphi }\) are tracial, e.g. \(\mathbb {G}\) is a unimodular Kac algebra. We prove that for \(1
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Phase Retrieval for Nilpotent Groups J. Fourier Anal. Appl. (IF 1.2) Pub Date : 2023-07-27 Hartmut Führ, Vignon Oussa
We study the phase retrieval property for orbits of general irreducible representations of nilpotent groups, for the classes of simply connected Lie groups, and for finite groups. We prove by induction that in the Lie group case, all irreducible representations do phase retrieval. For the finite group case, we mostly focus on p-groups. Here our main result states that every irreducible representation
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Beurling-Type Density Criteria for System Identification J. Fourier Anal. Appl. (IF 1.2) Pub Date : 2023-07-26 Céline Aubel, Helmut Bölcskei, Verner Vlačić
This paper addresses the problem of identifying a linear time-varying (LTV) system characterized by a (possibly infinite) discrete set of delay-Doppler shifts without a lattice (or other “geometry-discretizing”) constraint on the support set. Concretely, we show that a class of such LTV systems is identifiable whenever the upper uniform Beurling density of the delay-Doppler support sets, measured “uniformly
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The $$ L^1 $$ -Liouville Property on Graphs J. Fourier Anal. Appl. (IF 1.2) Pub Date : 2023-07-20 Andrea Adriani, Alberto G. Setti
In this paper we investigate the \( L^1 \)-Liouville property, underlining its connection with stochastic completeness and other structural features of the graph. We give a characterization of the \( L^1 \)-Liouville property in terms of the Green function of the graph and use it to prove its equivalence with stochastic completeness on model graphs. Moreover, we show that there exist stochastically
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New Error Bounds for Legendre Approximations of Differentiable Functions J. Fourier Anal. Appl. (IF 1.2) Pub Date : 2023-07-07 Haiyong Wang
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Power Spectrum Unbiasing for Dilation-Invariant Multi-reference Alignment J. Fourier Anal. Appl. (IF 1.2) Pub Date : 2023-07-08 Matthew Hirn, Anna Little
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New Lower Bounds for the Integration of Periodic Functions J. Fourier Anal. Appl. (IF 1.2) Pub Date : 2023-07-05 David Krieg, Jan Vybíral
We study the integration problem on Hilbert spaces of (multivariate) periodic functions.The standard technique to prove lower bounds for the error of quadrature rules uses bump functions and the pigeon hole principle. Recently, several new lower bounds have been obtained using a different technique which exploits the Hilbert space structure and a variant of the Schur product theorem. The purpose of
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Haar Frame Characterizations of Besov–Sobolev Spaces and Optimal Embeddings into Their Dyadic Counterparts J. Fourier Anal. Appl. (IF 1.2) Pub Date : 2023-06-15 Gustavo Garrigós, Andreas Seeger, Tino Ullrich
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Multilinear Pseudo-differential Operators with $$S_{0,0}$$ Class Symbols of Limited Smoothness J. Fourier Anal. Appl. (IF 1.2) Pub Date : 2023-06-16 Tomoya Kato
We consider the boundedness of the multilinear pseudo-differential operators with symbols in the multilinear Hörmander class \(S_{0,0}\). The aim of this paper is to discuss smoothness conditions for symbols to assure the boundedness between local Hardy spaces.
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Nuclear Fourier Transforms J. Fourier Anal. Appl. (IF 1.2) Pub Date : 2023-06-13 Dorothee D. Haroske, Leszek Skrzypczak, Hans Triebel
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Almost Everywhere Convergence for Lebesgue Differentiation Processes Along Rectangles J. Fourier Anal. Appl. (IF 1.2) Pub Date : 2023-06-12 E. D’Aniello, A. Gauvan, L. Moonens, J. Rosenblatt
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Affine Phase Retrieval for Sparse Signals via $$\ell _1$$ Minimization J. Fourier Anal. Appl. (IF 1.2) Pub Date : 2023-06-12 Meng Huang, Shixiang Sun, Zhiqiang Xu
Affine phase retrieval is the problem of recovering signals from the magnitude-only measurements with a priori information. In this paper, we use the \(\ell _1\) minimization to exploit the sparsity of signals for affine phase retrieval, showing that \(O(k\log ( en/k))\) Gaussian random measurements are sufficient to recover all k-sparse signals by solving a natural \(\ell _1\) minimization program
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Gagliardo–Nirenberg Inequalities in Lorentz Type Spaces J. Fourier Anal. Appl. (IF 1.2) Pub Date : 2023-06-06 Wei Wei, Yanqing Wang, Yulin Ye
In this paper, we derive some new Gagliardo–Nirenberg type inequalities in Lorentz type spaces without restrictions on the second index of Lorentz norms, which generalize almost all known corresponding results. Our proof mainly relies on the Bernstein inequalities in Lorentz spaces, the embedding relation among various Lorentz type spaces, and Littlewood–Paley decomposition techniques.
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Invertibility of Positive Toeplitz Operators and Associated Uncertainty Principle J. Fourier Anal. Appl. (IF 1.2) Pub Date : 2023-05-30 A. Walton Green, Mishko Mitkovski
We study invertibility and compactness of positive Toeplitz operators associated to a continuous Parseval frame on a Hilbert space. As applications, we characterize compactness of affine and Weyl-Heisenberg localization operators as well as give uncertainty principles for the associated transforms.
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Euler–MacLaurin Summation Formula on Polytopes and Expansions in Multivariate Bernoulli Polynomials J. Fourier Anal. Appl. (IF 1.2) Pub Date : 2023-05-30 L. Brandolini, L. Colzani, B. Gariboldi, G. Gigante, A. Monguzzi
We provide a multidimensional weighted Euler–MacLaurin summation formula on polytopes and a multidimensional generalization of a result due to L. J. Mordell on the series expansion in Bernoulli polynomials. These results are consequences of a more general series expansion; namely, if \(\chi _{\tau {\mathcal {P}}}\) denotes the characteristic function of a dilated integer convex polytope \({\mathcal
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Global Operator Calculus on Spin Groups J. Fourier Anal. Appl. (IF 1.2) Pub Date : 2023-05-17 P. Cerejeiras, M. Ferreira, U. Kähler, J. Wirth