Related papers: Some mudular inequalities in Lebesgue spaces with …
In this article we investigate an action of some operators (not necessary to be linear or sublinear) in the so-called (Bilateral) Grand Lebesgue Spaces (GLS), in particular, double weight Fourier operators, maximal operators, imbedding…
In this paper, we introduce a new class of convolution-type inequalities in variable exponent Lebesgue spaces and derive several related estimates, including the \(L^{r(\cdot)}\)--\(L^{p(\cdot)}\) smoothing estimate for the fractional heat…
We present a new approach to the question of when the commutativity of operator exponentials implies that of the operators. This is proved in the setting of bounded normal operators on a complex Hilbert space. The proofs are based on some…
We obtain one variant of the extrapolation theorem of Rubio de Fracia for variable exponent Lebesgue spaces. As a consequence we obtain conditions guarantee boundedness of strongly singular integral operators, singular integral operators…
In this article, we show that multilinear fractional type operators are bounded from product Hardy spaces with variable exponents into Lebesgue spaces with variable exponents via the atomic decomposition theory. We also study continuity…
In this work we obtain boundedness on weighted variable Lebesgue spaces of some maximal functions that come from the localized analysis considering a critical radius function. This analysis appears naturally in the context of the…
In this paper, the classical Dellacherie's theorem about stochastic process is extended to variable exponent Lebesgue spaces. As its applications, we obtain variable exponent analogues of several famous inequalities in classical martingale…
We obtain some new characterizations of a variable version of Lipschitz spaces in terms of the boundedness of commutators of sharp maximal functions, fractional maximal functions or fractional maximal commutators in the context of the…
The purpose of the present paper is to place a number of geometric (and hands-on) configurations relating to spectrum and geometry inside a general framework for the {\it Fuglede conjecture}. Note that in its general form, the Fuglede…
In this paper, we prove the boundedness of the Bergman projection on weighted mixed norm spaces of the upper-half space for some weights that are constructed using the logarithm function and growth functions. Our necessary and sufficient…
We consider structured optimisation problems defined in terms of the sum of a smooth and convex function, and a proper, l.s.c., convex (typically non-smooth) one in reflexive variable exponent Lebesgue spaces $L_{p(\cdot)}(\Omega)$. Due to…
Basic questions concerning nonsingular multilinear operators with oscillatory factors are posed and partially answered. Lebesgue space norm inequalities are established for multilinear integral operators of Calderon-Zygmund type which…
We characterize the class of weights related to the boundedness of variable fractional maximal operator $M_{\beta(\cdot),r(\cdot)}$ on variable Lebesgue spaces. This extend previously known results, including those corresponding to the…
In this article we introduce Variable exponent Fock spaces and study some of their basic properties such as the boundedness of evaluation functionals, density of polynomials, boundedness of a Bergman-type projection and duality.
Mixed-norm Lebesgue spaces found their place in the study of some questions in the theory of partial differential equations, as can be seen from recent interest in the continuity of certain classes of pseudodifferential operators on these…
In this paper we study some estimates of norms in variable exponent Lebesgue spaces for maximal multiplier operators.We will consider the case when multiplier is the Fourier transform of a compactly supported Borel measure
In this paper, we investigate the inequality \begin{equation*} \left\Vert f(\cdot +h)\right\Vert_{p\left( \cdot \right) }\leq A\left\Vert f\right\Vert_{p\left( \cdot \right) },\quad h\in \mathbb{R}^{n}, A>0 \end{equation*} under some…
In this article we obtain an "off-diagonal" version of the Fefferman-Stein vector-valued maximal inequality on weighted Lebesgue spaces with variable exponents. As an application of this result and the atomic decomposition developed in [12]…
We study the dual space of the variable Lebesgue space $\Lp$ with unbounded exponent function $\pp$ and provide an answer to a question posed in~[fiorenza-cruzuribe2013]. Our approach is to decompose the dual into a topological direct sum…
In this paper, we prove the Hardy-Leray inequality and related inequalities in variable Lebesgue spaces. Our proof is based on a version of the Stein-Weiss inequality in variable Lebesgue spaces derived from two weight inequalities due to…