Variable Exponent Spaces Research Articles

Syarat Cukup Ketaksamaan Holder di Ruang Lebesgue dengan Variabel Eksponen

Hӧlder inequality is a basic inequality in functional analysis. The inequality used for proofing other inequalities. In this research, the development of the application of the Hӧlder inequality in the Lebesgue spaces with variable exponent and Morrey spaces with variable exponent. The integral Hӧlder inequality is used because the Lebesgue spaces with variable exponent and Morrey spaces with variable exponent is a function space.This research shows the sufficient condition of Hӧlder inequality in Lebesgue spaces with variable exponent and the Morrey spaces with variable exponent according to the norm of the function and its characteristics.

Boundedness of Nonregular Pseudo-differential Operators and Their Adjoints on Variable Exponent Besov-Morrey Spaces

This paper deal with the boundedness property of non regular pseudo-differential operators a(x, D) and their adjoints a(x, D)* on variable exponent BM spaces. For this purpose, given such an operator, we use the technique of decomposition of its symbol into elementary symbols already used in other spaces.

Modular Geometric Properties in Variable Exponent Spaces

Much has been written on variable exponent spaces in recent years. Most of the literature deals with the normed space structure of such spaces. However, because of the variability of the exponent, the underlying modular structure of these spaces is radically different from that induced by the norm. In this article, we focus our attention on the progress made toward the study of the modular structure of the sequence Lebesgue spaces of variable exponents. In particular, we present a survey of the state of the art regarding modular geometric properties in variable exponent spaces.

Weak compactness and representation in variable exponent Lebesgue spaces on infinite measure spaces

Relative weakly compact sets and weak convergence in variable exponent Lebesgue spaces {L^{p(cdot )}(Omega )} for infinite measure spaces (Omega ,mu ) are characterized. Criteria recently obtained in [14] for finite measures are here extended to the infinite measure case. In particular, it is showed that the inclusions between variable exponent Lebesgue spaces for infinite measures are never L-weakly compact. A lattice isometric representation of {L^{p(cdot )}(Omega )} as a variable exponent space L^{q(cdot )}(0,1) is given.

Generalized fractional integral operators on variable exponent Morrey spaces of an integral form

Generalized fractional integral operators on variable exponent Morrey spaces of an integral form

New Modular Fixed-Point Theorem in the Variable Exponent Spaces ℓp(.)

In this work, we prove a fixed-point theorem in the variable exponent spaces ℓp(.), when p−=1 without further conditions. This result is new and adds more information regarding the modular structure of these spaces. To be more precise, our result concerns ρ-nonexpansive mappings defined on convex subsets of ℓp(.) that satisfy a specific condition which we call “condition of uniform decrease”.

Measure data elliptic problems with generalized Orlicz growth

We study nonlinear measure data elliptic problems involving the operator of generalized Orlicz growth. Our framework embraces reflexive Orlicz spaces, as well as natural variants of variable exponent and double-phase spaces. Approximable and renormalized solutions are proven to exist and coincide for arbitrary measure datum and to be unique when for a class of data being diffuse with respect to a relevant nonstandard capacity. A capacitary characterization of diffuse measures is provided.

Boundedness of Nonregular Pseudo-differential Operators on Variable Exponent Triebel-Lizorkin-Morrey Spaces

In this paper, we study the boundedness of non regular pseudo-differential operators on variable exponent Besov-Morrey spaces E s(·) p(·),u(·),q(·) with symbols a(x, ξ) belonging to C ℓ ∗S m 1,δ. For these symbols x-regularity is measured in H¨older-Zygmund spaces.

Poincaré inequalities and Neumann problems for the variable exponent setting

<abstract><p>In an earlier paper, Cruz-Uribe, Rodney and Rosta proved an equivalence between weighted Poincaré inequalities and the existence of weak solutions to a family of Neumann problems related to a degenerate $ p $-Laplacian. Here we prove a similar equivalence between Poincaré inequalities in variable exponent spaces and solutions to a degenerate $ {p(\cdot)} $-Laplacian, a non-linear elliptic equation with nonstandard growth conditions.</p></abstract>

Existence and nonexistence of solutions of thin-film equations with variable exponent spaces

Existence and nonexistence of solutions of thin-film equations with variable exponent spaces

Existence of tumor invasion model with mesenchymal and epithelial transition processes in variable exponent spaces

This work illustrate the solvability of the system consist of tumor cells of two types along with epithelial cells and mesenchymal densities. The role of proteins matrix metalloproteinases and extra cellular matrix are considered. Along with the square integrability of the mesenchymal epithelial transition function, the solvability is illustrated under the Faedo–Galerkin approximation method.

The Spectrum of Mapping Ideals of Type Variable Exponent Function Space of Complex Variables with Some Applications

The topological and geometric behaviors of the variable exponent formal power series space, as well as the prequasi-ideal construction by s -numbers and this function space of complex variables, are investigated in this article. Upper bounds for s -numbers of infinite series of the weighted n th power forward and backward shift operator on this function space are being investigated, with applications to some entire functions.

Periodic Points of Modular Firmly Mappings in the Variable Exponent Sequence Spaces ℓp(·)

In this work, we investigate the existence of periodic points of mappings defined on nonconvex domains within the variable exponent sequence spaces ℓp(·). In particular, we consider the case of modular firmly nonexpansive and modular firmly asymptotically nonexpansive mappings. These kinds of results have never been obtained before.

Relatively Compact Sets in Variable Exponent Morrey Spaces on Metric Spaces

We study a characterization of the precompactness of sets in variable exponent Morrey spaces on bounded metric measure spaces. Totally bounded sets are characterized from several points of view for the case of variable exponent Morrey spaces over metric measure spaces. This characterization is new in the case of constant exponents.

Existence and multiplicity of solutions for Kirchhoff-type potential systems with variable critical growth exponent

In this paper, by using the concentration-compactness principle of Lions for variable exponents found in [Bonder JF, Silva A. Concentration-compactness principal for variable exponent space and applications. Electron J Differ Equ. 2010;141:1–18.] and the Mountain Pass Theorem without the Palais–Smale condition given in [Rabinowitz PH. Minimax Methods in Critical Point Theory with Applications to Differential Equations, CBMS Reg. Conf. Ser. Math., Vol. 65, Amer. Math. Soc., Providence, RI, 1986.], we obtain the existence and multiplicity solutions , for a class of Kirchhoff-Type Potential Systems with critical exponent, namely where Ω is a bounded smooth domain in , and The functions , , and () are given functions, whose properties will be introduced hereafter, λ is the positive parameter, and the real function F belongs to , denotes the partial derivative of F with respect to . Our results extend, complement and complete in several ways some of many works in particular [Chems Eddine N. Existence of solutions for a critical (p1(x), . , pn(x))-Kirchhoff-type potential systems. Appl Anal. 2020.]. We want to emphasize that a difference of some previous research is that the conditions on are general enough to incorporate some differential operators of great interest. In particular, we can cover a general class of nonlocal operators for for all .

The inclusion theorems for generalized variable exponent grand Lebesgue spaces

In this paper, we discuss and investigate the existence of the inclusion $ L^{p(.),\theta }\left( \mu \right) \subseteq L^{q(.),\theta }\left( \nu \right) $, where $\mu $ and $\nu $ are two finite measures on $\left( X,\Sigma \right) .$ Moreover, we show that the generalized variable exponent grand Lebesgue space$ L^{p(.),\theta }\left( \Omega \right) $ has a potential-type approximate identity, where $\Omega $ is a bounded open subset of $ \mathbb{R}^{d}.$

Addendum to “On the Riesz potential operator of variable order from variable exponent Morrey space to variable exponent Campanato space”, Math Meth Appl Sci. 2020; 1–8

In the paper mentioned in the title, it is proved the boundedness of the Riesz potential operator of variable order α(x) from variable exponent Morrey space to variable exponent Campanato space, under certain assumptions on the variable exponents p(x) and λ(x) of the Morrey space. Assumptions on the exponents were different depending on whether takes or not the critical values 0 or 1. In this note, we improve those results by unifying all the cases and covering the whole range . We also provide a correction to some minor technicality in the proof of Theorem 2 in the aforementioned paper.

Fractional operators of variable order from variable exponent Morrey spaces to variable exponent Campanato spaces on quasi-metric measure spaces with growth condition

Fractional operators of variable order from variable exponent Morrey spaces to variable exponent Campanato spaces on quasi-metric measure spaces with growth condition

On weak solutions for fourth‐order problems involving the Leray–Lions type operators

We investigate existence and multiplicity of weak solutions for fourth‐order problems involving the Leray–Lions type operators in variable exponent spaces and improve a result of Bonanno and Chinnì (2011). We use variational methods and apply a multiplicity theorem of Bonanno and Marano (2010).

On a class of sublinear operators in variable exponent Morrey-type spaces

For a class of sublinear operators, we find conditions on the variable exponent Morrey-type space ensuring the boundedness in this space. A priori assumptions on this class are that the operators are bounded in and satisfy some size condition. This class includes in particular the maximal operator, singular operators with the standard kernel, and the Hardy operators. We also prove embedding of variable exponent Morrey-type spaces into weighted -spaces.