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Zero volume boundary for extension domains from Sobolev to BV Rev. Mat. Complut. (IF 0.8) Pub Date : 2024-02-08 Tapio Rajala, Zheng Zhu
In this note, we prove that the boundary of a \((W^{1, p}, BV)\)-extension domain is of volume zero under the assumption that the domain \({\Omega }\) is 1-fat at almost every \(x\in \partial {\Omega }\). Especially, the boundary of any planar \((W^{1, p}, BV)\)-extension domain is of volume zero.
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On smooth functions with two critical values Rev. Mat. Complut. (IF 0.8) Pub Date : 2024-01-24 Antonio Lerario, Chiara Meroni, Daniele Zuddas
We prove that every smooth closed connected manifold admits a smooth real-valued function with only two critical values such that the set of minima (or maxima) can be arbitrarily prescribed, as soon as this set is a finite subcomplex of the manifold (we call a function of this type a Reeb function). In analogy with Reeb’s Sphere Theorem, we use such functions to study the topology of the underlying
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Linear representations of fundamental groups of Klein surfaces derived from spinor representations of Clifford algebras Rev. Mat. Complut. (IF 0.8) Pub Date : 2023-12-27 Ewa Tyszkowska
We study actions of multiplicative subgroups of Clifford algebras on Riemann surfaces. We show that every Klein surface of algebraic genus greater than 1 is isomorphic to the orbit space of such an action. We obtain linear representations of fundamental groups of Klein surfaces by using the spinor representations of Clifford algebras.
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Non-negative solutions and strong maximum principle for a resonant quasilinear problem Rev. Mat. Complut. (IF 0.8) Pub Date : 2023-10-03 Giovanni Anello, Filippo Cammaroto, Luca Vilasi
We study the resonant quasilinear problem $$\begin{aligned} -\Delta _p u = \lambda _p u^{p-1} + \lambda g(u) \text { in } \Omega ,\;\; u\ge 0 \text { in } \Omega , \;\; u_{|\partial \Omega }=0, \end{aligned}$$ where \(\Omega \subset {\mathbb {R}}^N\) is a smooth, bounded domain, \(\lambda _p\) is the first eigenvalue of \(-\Delta _p\) in \(\Omega \), and \(g:[0,+\infty )\rightarrow {\mathbb {R}}\)
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Some recent developments on the Steklov eigenvalue problem Rev. Mat. Complut. (IF 0.8) Pub Date : 2023-09-28 Bruno Colbois, Alexandre Girouard, Carolyn Gordon, David Sher
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Smooth norms in dense subspaces of $$\ell _p(\Gamma )$$ and operator ranges Rev. Mat. Complut. (IF 0.8) Pub Date : 2023-08-22 Sheldon Dantas, Petr Hájek, Tommaso Russo
For \(1\le p<\infty \), we prove that the dense subspace \(\mathcal {Y}_p\) of \(\ell _p(\Gamma )\) comprising all elements y such that \(y \in \ell _q(\Gamma )\) for some \(q \in (0,p)\) admits a \(C^{\infty }\)-smooth norm which locally depends on finitely many coordinates. Moreover, such a norm can be chosen as to approximate the \(\left\| \cdot \right\| _p\)-norm. This provides examples of dense
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On the reduced Bernstein-Sato polynomial of Thom-Sebastiani singularities Rev. Mat. Complut. (IF 0.8) Pub Date : 2023-08-10 A. Castaño Domínguez, L. Narváez Macarro
Given two holomorphic functions f and g defined in two respective germs of complex analytic manifolds (X, x) and (Y, y), we know thanks to M. Saito that, as long as one of them is Euler homogeneous, the reduced (or microlocal) Bernstein-Sato polynomial of the Thom-Sebastiani sum \(f+g\) can be expressed in terms of those of f and g. In this note we give a purely algebraic proof of a similar relation
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Ranks of maps of vector bundles Rev. Mat. Complut. (IF 0.8) Pub Date : 2023-07-10 Montserrat Teixidor i Bigas
We generalize to vector bundles the techniques introduced for line bundles in Liu (TAMS 374:367–405, 2021). We then use this method to prove the injectivity of the Petri map for vector bundles and the surjectivity of a map related to deformation theory of Poincaré sheaves.
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New examples of harmonic maps to the hyperbolic plane via Bäcklund transformation Rev. Mat. Complut. (IF 0.8) Pub Date : 2023-06-21 G. Polychrou, E. Papageorgiou, A. Fotiadis, C. Daskaloyannis
We study harmonic maps from a subset of the complex plane to a subset of the hyperbolic plane. In Fotiadis and Daskaloyannis (Nonlinear Anal 214, 112546, 2022), harmonic maps are related to the sinh-Gordon equation and a Bäcklund transformation is introduced, which connects solutions of the sinh-Gordon and sine-Gordon equation. We develop this machinery in order to construct new harmonic maps to the
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Equivalent characterizations of martingale Hardy–Lorentz spaces with variable exponents Rev. Mat. Complut. (IF 0.8) Pub Date : 2023-06-02 Ferenc Weisz
We prove that under the log-Hölder continuity condition of the variable exponent \(p(\cdot )\), a new type of maximal operators, \(U_{\gamma ,s}\) is bounded from the variable martingale Hardy–Lorentz space \(H_{p(\cdot ),q}\) to \(L_{p(\cdot ),q}\), whenever \(0
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Algebraic valuation ring extensions as limits of complete intersection algebras Rev. Mat. Complut. (IF 0.8) Pub Date : 2023-05-31 Dorin Popescu
We show that an algebraic immediate valuation ring extension of characteristic \(p>0\) is a filtered union of complete intersection algebras of finite type.
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Strict $${\mathcal {C}}^p$$ -triangulations of sets locally definable in o-minimal structures with an application to a $$\mathcal C^p$$ -approximation problem Rev. Mat. Complut. (IF 0.8) Pub Date : 2023-05-29 Wiesław Pawłucki
We show how to derive triangulations of sets locally definable in o-minimal structures from triangulations of compact definable sets. We give it in particular for strict \(\mathcal C^p\)-triangulations which has been recently studied by the author. This combined with a theorem of Fernando and Ghiloni implies that every continuous mapping defined on a locally compact subset B of \(\mathbb R^m\) with
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Terracini loci of curves Rev. Mat. Complut. (IF 0.8) Pub Date : 2023-05-25 Edoardo Ballico, Luca Chiantini
We study subsets S of curves X whose double structure does not impose independent conditions to a linear series L, but there are divisors \(D\in |L|\) singular at all points of S. These subsets form the Terracini loci of X. We investigate Terracini loci, with a special look towards their non-emptiness, mainly in the case of canonical curves, and in the case of space curves.
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Poincaré–Reeb graphs of real algebraic domains Rev. Mat. Complut. (IF 0.8) Pub Date : 2023-05-23 Arnaud Bodin, Patrick Popescu-Pampu, Miruna-Ştefana Sorea
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Variable exponent Sobolev spaces and regularity of domains-II Rev. Mat. Complut. (IF 0.8) Pub Date : 2023-05-17 Przemysław Górka, Nijjwal Karak, Daniel J. Pons
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Mixed norm spaces and RM(p, q) spaces Rev. Mat. Complut. (IF 0.8) Pub Date : 2023-05-12 Tanausú Aguilar-Hernández
In this paper we present the containment relationship between the spaces of analytic functions with average radial integrability RM(p, q) and a family of mixed norm spaces.
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A monotonicity result for the first Steklov–Dirichlet Laplacian eigenvalue Rev. Mat. Complut. (IF 0.8) Pub Date : 2023-04-30 Nunzia Gavitone, Gianpaolo Piscitelli
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Symmetric finite representability of $$\ell ^p$$ -spaces in rearrangement invariant spaces on [0, 1] Rev. Mat. Complut. (IF 0.8) Pub Date : 2023-04-14 Sergey V. Astashkin, Guillermo P. Curbera
For a separable rearrangement invariant space X on [0, 1] of fundamental type we identify the set of all \(p\in [1,\infty ]\) such that \(\ell ^p\) is finitely represented in X in such a way that the unit basis vectors of \(\ell ^p\) (\(c_0\) if \(p=\infty \)) correspond to pairwise disjoint and equimeasurable functions. This can be treated as a follow up of a paper by the first-named author related
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Deformations and moduli of irregular canonical covers with $$K^2=4p_g-8$$ Rev. Mat. Complut. (IF 0.8) Pub Date : 2023-03-21 Purnaprajna Bangere, Francisco Javier Gallego, Jayan Mukherjee, Debaditya Raychaudhury
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A note on the supersolution method for Hardy’s inequality Rev. Mat. Complut. (IF 0.8) Pub Date : 2023-03-10 Francesca Bianchi, Lorenzo Brasco, Firoj Sk, Anna Chiara Zagati
We prove a characterization of Hardy’s inequality in Sobolev–Slobodeckiĭ spaces in terms of positive local weak supersolutions of the relevant Euler-Lagrange equation. This extends previous results by Ancona Kinnunen & Korte for standard Sobolev spaces. The proof is based on variational methods.
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A homeomorphism theorem for sums of translates Rev. Mat. Complut. (IF 0.8) Pub Date : 2023-03-04 Bálint Farkas, Béla Nagy, Szilárd Gy. Révész
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Cross-caps, triple points and a linking invariant for finitely determined germs Rev. Mat. Complut. (IF 0.8) Pub Date : 2023-02-17 Gergő Pintér, András Sándor
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Some properties of differentiable p-adic functions Rev. Mat. Complut. (IF 0.8) Pub Date : 2023-02-09 J. Fernández-Sánchez, S. Maghsoudi, D. L. Rodríguez-Vidanes, J. B. Seoane–Sepúlveda
In this paper, using the tools from the lineability theory, we distinguish certain subsets of p-adic differentiable functions. Specifically, we show that the following sets of functions are large enough to contain an infinite dimensional algebraic structure: (i) continuously differentiable but not strictly differentiable functions, (ii) strictly differentiable functions of order r but not strictly
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Two theorems on the intersections of horospheres in asymptotically harmonic spaces Rev. Mat. Complut. (IF 0.8) Pub Date : 2023-02-03 Sinhwi Kim, JeongHyeong Park
We use Busemann functions to construct volume preserving mappings in an asymptotically harmonic manifold. If the asymptotically harmonic manifold satisfies the visibility condition, we construct mappings which preserve distances in some directions. We also prove that some integrals on the intersection of horospheres are independent of the differences between the values of the corresponding Busemann
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The asymptotic Samuel function and invariants of singularities Rev. Mat. Complut. (IF 0.8) Pub Date : 2023-02-02 A. Benito, A. Bravo, S. Encinas
The asymptotic Samuel function generalizes to arbitrary rings the usual order function of a regular local ring. In this paper, we use this function to introduce the notion of the Samuel slope of a Noetherian local ring, and we study some of its properties. In particular, we focus on the case of a local ring at singular point of a variety, and, among other results, we prove that the Samuel slope of
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Critical metrics for quadratic curvature functionals on some solvmanifolds Rev. Mat. Complut. (IF 0.8) Pub Date : 2023-01-17 Giovanni Calvaruso, Amirhesam Zaeim
We prove the existence of four-dimensional compact manifolds admitting some non-Einstein Lorentzian metrics, which are critical points for all quadratic curvature functionals. For this purpose, we consider left-invariant semi-direct extensions \(G_{\mathcal S}=H \rtimes \exp ({\mathbb {R}}S)\) of the Heisenberg Lie group H, for any \(\mathcal S \in {\mathfrak {s}}{\mathfrak {p}}(1,\mathbb R)\), equipped
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Existence and multiplicity of solutions to p-Laplacian equations on graphs Rev. Mat. Complut. (IF 0.8) Pub Date : 2023-01-13 Mengqiu Shao
In this paper, we investigate the existence of multiple solutions to the nonlinear p-Laplacian equation $$\begin{aligned} -\Delta _{p} u +h(x)|u|^{p-2}u= f(x,u)+g(x) \end{aligned}$$ on the locally finite graph G, where \(\Delta _{p}\) is the discrete p-Laplacian on graphs, \(p\ge 2\). Under more general conditions, we prove that the p-Laplacian equation admits at least two nontrivial different solutions
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On a special class of non-local variational problems Rev. Mat. Complut. (IF 0.8) Pub Date : 2023-01-13 Pablo Pedregal
Non-local variational problems where non-locality is expressed in a special form are considered. In addition to introducing non-local spaces as the natural ambient spaces for such variational problems, we establish two surprising facts. (1) A way to clearly show the difference with local problems as linear functions are shown not to be minimizers for the Dirichlet, non-local integral under boundary
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Multiple solutions for nonlinear boundary value problems of Kirchhoff type on a double phase setting Rev. Mat. Complut. (IF 0.8) Pub Date : 2023-01-09 Alessio Fiscella, Greta Marino, Andrea Pinamonti, Simone Verzellesi
This paper deals with some classes of Kirchhoff type problems on a double phase setting and with nonlinear boundary conditions. Under general assumptions, we provide multiplicity results for such problems in the case when the perturbations exhibit a suitable behavior in the origin and at infinity, or when they do not necessarily satisfy the Ambrosetti–Rabinowitz condition. To this aim, we combine variational
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An anisotropic summability and mixed sequences Rev. Mat. Complut. (IF 0.8) Pub Date : 2023-01-05 Jamilson R. Campos, Renato Macedo, Joedson Santos
In this paper we define and study a vector-valued sequence space, called the space of anisotropic (s, q, r)-summable sequences, that generalizes the classical space of (s; q)-mixed sequences (or mixed (s; q)-summable sequences). Furthermore, we define two classes of linear operators involving this new space and one of them generalizes the class of (s; q) -mixed linear operators due A. Pietsch. Some
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Multiple normalized solutions for the coupled Hartree–Fock system with upper critical exponent Rev. Mat. Complut. (IF 0.8) Pub Date : 2023-01-04 Shuai Yao, Haibo Chen
In the present paper, we are concerned with the existence and multiplicity of normalized solutions of coupled Hartree–Fock system with upper critical exponent and lower power perturbation. This type system arises from the basic quantum chemistry model of small number of electrons interacting with static nuclei which can be approximated by Hartree or Hartree–Fock minimization problems. First, by constraint
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Evaluating recent methods to overcome spatial confounding Rev. Mat. Complut. (IF 0.8) Pub Date : 2022-12-25 Arantxa Urdangarin, Tomás Goicoa, María Dolores Ugarte
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On the reflexivity of the spaces of variable integrability and summability Rev. Mat. Complut. (IF 0.8) Pub Date : 2022-11-21 Arash Ghorbanalizadeh, Reza Roohi Seraji, Yoshihiro Sawano
In this paper, we show that under the condition \( 1
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Existence and multiplicity of solutions for a singular anisotropic problem with a sign-changing term Rev. Mat. Complut. (IF 0.8) Pub Date : 2022-11-16 Francisco Julio S. A. Corrêa, Gelson C. G. dos Santos, Leandro S. Tavares
In this paper we investigate the existence and multiplicity of solutions for a class of singular anisotropic problems involving a weight and a term that may change sign. The approach is based on sub-supersolutions and the Mountain Pass Theorem.
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On the Crawford number attaining operators Rev. Mat. Complut. (IF 0.8) Pub Date : 2022-11-04 Geunsu Choi, Han Ju Lee
We study the denseness of Crawford number attaining operators on Banach spaces. Mainly, we prove that if a Banach space has the Radon–Nikodým property, then the set of Crawford number attaining operators is dense in the space of bounded linear operators. We also see among others that the set of Crawford number attaining operators is dense in the space of all bounded linear operators while they do not
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D’Atri spaces and the total scalar curvature of hemispheres, tubes and cylinders Rev. Mat. Complut. (IF 0.8) Pub Date : 2022-10-10 Balázs Csikós, Amr Elnashar, Márton Horváth
Csikós and Horváth proved in J Geom Anal 28(4): 3458-3476, (2018) that if a connected Riemannian manifold of dimension at least 4 is harmonic, then the total scalar curvatures of tubes of small radius about an arbitrary regular curve depend only on the length of the curve and the radius of the tube, and conversely, if the latter condition holds for cylinders, i.e., for tubes about geodesic segments
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Liouville theorem for Hénon-Hardy systems in the unit ball Rev. Mat. Complut. (IF 0.8) Pub Date : 2022-10-09 Phuong Le
Let (u, v) be a nonnegative solution to the system $$\begin{aligned} (-\Delta )^\frac{\alpha }{2} u = |x|^a v^p, \quad (-\Delta )^\frac{\beta }{2} v = |x|^b u^q \end{aligned}$$ in the unit ball with the Navier boundary condition, where \(\alpha ,\beta ,a,b\) are real numbers such that \(\alpha ,\beta \in (0,n)\), \(a>-\alpha \) and \(b>-\beta \). By exploiting the method of scaling spheres in integral
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Deformations of vector bundles over Lie groupoids Rev. Mat. Complut. (IF 0.8) Pub Date : 2022-09-23 Pier Paolo La Pastina, Luca Vitagliano
VB-groupoids are vector bundles in the category of Lie groupoids. They encompass several classical objects, including Lie group representations and 2-vector spaces. Moreover, they provide geometric pictures for 2-term representations up to homotopy of Lie groupoids. We attach to every VB-groupoid a cochain complex controlling its deformations and discuss its fundamental features, such as Morita invariance
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Some q-supercongruences from the Gasper and Rahman quadratic summation Rev. Mat. Complut. (IF 0.8) Pub Date : 2022-09-23 Victor J. W. Guo
We give four families of q-supercongruences modulo the square and cube of a cyclotomic polynomial from Gasper and Rahman’s quadratic summation. As conclusions, we obtain four new supercongruences modulo \(p^2\) or \(p^3\), such as: for \(d \ge 2, r \ge 1\) with \(\gcd (d,r)=1\) and \(d+r\) odd, and any prime \(p\equiv d+r\pmod {2d}\) with \(p\geqslant d+r\), $$\begin{aligned} \sum _{k=0}^{p-1}(3dk+r)\frac{
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Kirby diagrams and 5-colored graphs representing compact 4-manifolds Rev. Mat. Complut. (IF 0.8) Pub Date : 2022-08-29 Maria Rita Casali, Paola Cristofori
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Stability results on the Kirchhoff plate equation with delay terms on the dynamical boundary controls Rev. Mat. Complut. (IF 0.8) Pub Date : 2022-08-18 Mohammad Akil, Haidar Badawi, Serge Nicaise, Ali Wehbe
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Convexity of ratios of the modified Bessel functions of the first kind with applications Rev. Mat. Complut. (IF 0.8) Pub Date : 2022-08-09 Zhen-Hang Yang, Jing-Feng Tian
Let \(I_{\nu }\left( x\right) \) be the modified Bessel function of the first kind of order \(\nu \). Motivated by a conjecture on the convexity of the ratio \(W_{\nu }\left( x\right) =xI_{\nu }\left( x\right) /I_{\nu +1}\left( x\right) \) for \(\nu >-2\), using the monotonicity rules for a ratio of two power series and an elementary technique, we present fully the convexity of the functions \(W_{\nu
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Sturm attractors for fully nonlinear parabolic equations Rev. Mat. Complut. (IF 0.8) Pub Date : 2022-08-03 Phillipo Lappicy
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The impact of the zero order term in the study of Dirichlet problems with convection or drift terms Rev. Mat. Complut. (IF 0.8) Pub Date : 2022-07-20 Lucio Boccardo
In this paper we study the impact of the zero order term in the study of Dirichlet problems with convection or drift terms.
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The k-nearest neighbors method in single index regression model for functional quasi-associated time series data Rev. Mat. Complut. (IF 0.8) Pub Date : 2022-07-06 Salim Bouzebda, Ali Laksaci, Mustapha Mohammedi
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A distributional approach to fractional Sobolev spaces and fractional variation: asymptotics I Rev. Mat. Complut. (IF 0.8) Pub Date : 2022-06-20 Giovanni E. Comi, Giorgio Stefani
We continue the study of the space \(BV^\alpha ({\mathbb {R}}^n)\) of functions with bounded fractional variation in \({\mathbb {R}}^n\) of order \(\alpha \in (0,1)\) introduced in our previous work (Comi and Stefani in J Funct Anal 277(10):3373–3435, 2019). After some technical improvements of certain results of Comi and Stefani (2019) which may be of some separated insterest, we deal with the asymptotic
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Anisotropic Dirichlet double phase problems with competing nonlinearities Rev. Mat. Complut. (IF 0.8) Pub Date : 2022-06-18 S. Leonardi, Nikolaos S. Papageorgiou
We consider a Dirichlet double phase problem with variable exponents and nonstandard growth. The reaction has the competing effects of a parametric concave term and a superlinear perturbation (“concave–convex problem”). We show that for all small values of the parameter the problem has at least two nontrivial bounded solutions.
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The class of c-almost periodic functions defined on vertical strips in the complex plane Rev. Mat. Complut. (IF 0.8) Pub Date : 2022-06-16 Hadjer Ounis, Juan Matías Sepulcre
In this paper, we develop the notion of c-almost periodicity for functions defined on vertical strips in the complex plane. As a generalization of Bohr’s concept of almost periodicity, we study the main properties of this class of functions which was recently introduced for the case of one real variable. In fact, we extend some important results of this theory which were already demonstrated for some
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Quantitative John–Nirenberg inequalities at different scales Rev. Mat. Complut. (IF 0.8) Pub Date : 2022-06-07 Javier C. Martínez-Perales, Ezequiel Rela, Israel P. Rivera-Ríos
Given a family \({\mathcal {Z}}=\{\Vert \cdot \Vert _{Z_Q}\}\) of norms or quasi-norms with uniformly bounded triangle inequality constants, where each Q is a cube in \({\mathbb {R}}^n\), we provide an abstract estimate of the form $$\begin{aligned} \Vert f-f_{Q,\mu }\Vert _{Z_Q}\le c(\mu )\psi ({\mathcal {Z}})\Vert f\Vert _{\mathrm {BMO}(\mathrm {d}\mu )} \end{aligned}$$ for every function \(f\in
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Meromorphic nearby cycle functors and monodromies of meromorphic functions (with Appendix by T. Saito) Rev. Mat. Complut. (IF 0.8) Pub Date : 2022-05-27 Tat Thang Nguyen, Kiyoshi Takeuchi
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Algebras and Banach spaces of Dirichlet series with maximal Bohr’s strip Rev. Mat. Complut. (IF 0.8) Pub Date : 2022-05-17 Thiago R. Alves, Leonardo Brito, Daniel Carando
We study linear and algebraic structures in sets of Dirichlet series with maximal Bohr’s strip. More precisely, we consider a set \({\mathscr {M}}\) of Dirichlet series which are uniformly continuous on the right half plane and whose strip of uniform but not absolute convergence has maximal width, i.e., \(\nicefrac {1}{2}\). Considering the uniform norm, we show that \({\mathscr {M}}\) contains an
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Log Fano blowups of mixed products of projective spaces and their effective cones Rev. Mat. Complut. (IF 0.8) Pub Date : 2022-05-18 Tim Grange, Elisa Postinghel, Artie Prendergast-Smith
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On the Michor–Mumford phenomenon in the infinite dimensional Heisenberg group Rev. Mat. Complut. (IF 0.8) Pub Date : 2022-05-16 Valentino Magnani, Daniele Tiberio
In the infinite dimensional Heisenberg group, we construct a left invariant weak Riemannian metric that gives a degenerate geodesic distance. The same construction yields a degenerate sub-Riemannian distance. We show how the standard notion of sectional curvature adapts to our framework, but it cannot be defined everywhere and it is unbounded on suitable sequences of planes. The vanishing of the distance
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Harmonic unit normal sections of Grassmannians associated with cross products Rev. Mat. Complut. (IF 0.8) Pub Date : 2022-04-26 Francisco Ferraris, Ruth Paola Moas, Marcos Salvai
Let \(G\left( k,n\right) \) be the Grassmannian of oriented subspaces of dimension k of \(\mathbb {R}^{n}\) with its canonical Riemannian metric. We study the energy of maps assigning to each \(P\in G\left( k,n\right) \) a unit vector normal to P. They are sections of a sphere bundle \(E_{k,n}^{1}\) over \(G\left( k,n\right) \). The octonionic double and triple cross products induce in a natural way
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The $$\mathbb Z$$ Z -genus of boundary links Rev. Mat. Complut. (IF 0.8) Pub Date : 2022-04-15 Peter Feller, JungHwan Park, Mark Powell
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On the weak convergence of shift operators to zero on rearrangement-invariant spaces Rev. Mat. Complut. (IF 0.8) Pub Date : 2022-03-22 Oleksiy Karlovych, Eugene Shargorodsky
Let \(\{h_n\}\) be a sequence in \({\mathbb {R}}^d\) tending to infinity and let \(\{T_{h_n}\}\) be the corresponding sequence of shift operators given by \((T_{h_n}f)(x)=f(x-h_n)\) for \(x\in {\mathbb {R}}^d\). We prove that \(\{T_{h_n}\}\) converges weakly to the zero operator as \(n\rightarrow \infty \) on a separable rearrangement-invariant Banach function space \(X({\mathbb {R}}^d)\) if and only
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Smooth quotients of generalized Fermat curves Rev. Mat. Complut. (IF 0.8) Pub Date : 2022-02-24 Rubén A. Hidalgo
A closed Riemann surface S is called a generalized Fermat curve of type (p, n), where \(n,p \ge 2\) are integers such that \((p-1)(n-1)>2\), if it admits a group \(H \cong {\mathbb Z}_{p}^{n}\) of conformal automorphisms with quotient orbifold S/H of genus zero with exactly \(n+1\) cone points, each one of order p; in this case H is called a generalized Fermat group of type (p, n). In this case, it
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On asymptotic behavior for a class of diffusion equations involving the fractional $$\wp (\cdot )$$ ℘ ( · ) -Laplacian as $$\wp (\cdot )$$ ℘ ( · ) goes to $$\infty $$ ∞ Rev. Mat. Complut. (IF 0.8) Pub Date : 2022-01-31 Lauren M. M. Bonaldo, Elard J. Hurtado
In this manuscript, we will study the asymptotic behavior for a class of nonlocal diffusion equations associated with the weighted fractional \(\wp (\cdot )\)-Laplacian operator involving constant/variable exponent, with \(\wp ^{-}:=\min _{(x,y) \in {\overline{\Omega }}\times {\overline{\Omega }}} \wp (x,y)\geqslant \max \left\{ 2N/(N+2s),1\right\} \) and \(s\in (0,1).\) In the case of constant exponents
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Carleman type inequalities for fractional relativistic operators Rev. Mat. Complut. (IF 0.8) Pub Date : 2022-01-31 Luz Roncal, Diana Stan, Luis Vega
In this paper we derive Carleman estimates for the fractional relativistic operator. We consider changing-sign solutions to the heat equation for such operators. We prove monotonicity inequalities and convexity of certain energy functionals to deduce Carleman estimates with linear exponential weight. Our approach is based on spectral methods and functional calculus.
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Stability of the inverses of interpolated operators with application to the Stokes system Rev. Mat. Complut. (IF 0.8) Pub Date : 2022-01-25 I. Asekritova, N. Kruglyak, M. Mastyło
We study the stability of isomorphisms between interpolation scales of Banach spaces, including scales generated by well-known interpolation methods. We develop a general framework for compatibility theorems, and our methods apply to general cases. As a by-product we prove that the interpolated isomorphisms satisfy uniqueness-of-inverses. We use the obtained results to prove the stability of lattice