Related papers: Dual spaces to Orlicz - Lorentz spaces

Certain inequalities between the values of the modular and the norm in the Orlicz spaces are established. These inequalities are applied then to the theory of solvability of nonlinear integral equations of Hammerstein type.

We characterize when an Orlicz space $L^A$ is almost compactly (uniformly absolutely continuously) embedded into a Lorentz space $L^{p,q}$ in terms of a balance condition involving parameters $p,q\in[1,\infty]$, and a Young function $A$. In…

Let $\Omega$ be either $\mathbb{R}^n$ or an unbounded strongly Lipschitz domain of $\mathbb{R}^n$, and $\Phi$ be a continuous, strictly increasing, subadditive and positive function on $(0,\infty)$ of upper type 1 and of strictly critical…

We deduce continuity properties for pseudo-differential operators with symbols in Orlicz modulation spaces when acting on other Orlicz modulation spaces. In particular we extend well-known results in the literature. We also show that the…

We characterize Ces\`aro-Orlicz function spaces $Ces_\varphi$ containing isomorphic copy of $l^\infty$. We also describe the subspaces $(Ces_\varphi)_a$ of all order continuous elements of $Ces_\varphi$. Finally, we study the monotonicity…

In this article we prove both norm and modular Hardy inequalities for a class functions in one-dimensional fractional Orlicz-Sobolev spaces.

We establish pointwise estimates expressed in terms of a nonlinear potential of a generalized Wolff type for $A$-superharmonic functions with nonlinear operator $A:\Omega\times\mathbb{R}^n\to\mathbb{R}^n$ having measurable dependence on the…

Let $\Bc$ denote the real-valued functions continuous on the extended real line and vanishing at $-\infty$. Let $\Br$ denote the functions that are left continuous, have a right limit at each point and vanish at $-\infty$. Define $\acn$ to…

Schauder Orlicz-type estimates are derived for weak solutions to second-order linear elliptic equations in divergence form with lower-order terms. The Orlicz setting $X=L^\psi$ is treated first. Under suitable assumptions on the Young…

We study the boundedness of intrinsic square functions and their commutators on generalized Orlicz-Morrey spaces $M^{\Phi,\varphi}(\mathbb{R}^n)$. In all the cases the conditions for the boundedness are given either in terms of Zygmund-type…

The general dual volume $\dveV(K)$ and the general dual Orlicz curvature measure $\deV(K, \cdot)$ were recently introduced for functions $G: (0, \infty)\times \sphere\rightarrow (0, \infty)$ and convex bodies $K$ in $\R^n$ containing the…

We study numerical integration of functions $f: \mathbb{R}^{s} \to \mathbb{R}$ with respect to a probability measure. By applying the corresponding inverse cumulative distribution function, the problem is transformed into integrating an…

We study singular integral operators with variable Calder\'on--Zygmund kernels and their commutators with $VMO$ functions in the framework of Orlicz spaces. After revisiting the classical $L^p$ theory, we establish boundedness results in…

In this paper, we extend the Marcinkiewicz--Zygmund inequality to the setting of Orlicz and Lorentz spaces. Furthermore, we generalize a Kadec--Pe{\l}czy\'nski-type result -- originally established by the first and third authors for $L^p$…

In this paper, we introduce Orlicz spaces on $ \mathbb Z^n \times \mathbb T^n $ and Orlicz modulation spaces on $\mathbb Z^n$, and present some basic properties such as inclusion relations, convolution relations, and duality of these…

(Two-scale) gradient Young measures in Orlicz-Sobolev setting are introduced and characterized providing also an integral representation formula for non convex energies arising in homogenization problems with nonstandard growth.

The goal of this paper is to present an isometric representation of the dual space to Ces\`aro function space $C_{p,w}$, $1<p<\infty$, induced by arbitrary positive weight function $w$ on interval $(0,l)$ where $0<l\leqslant\infty$. For…

In the paper, we analyze the Lebesgue exponents $p_\Phi$ and $q_\Phi$, and show that for any $p_\Phi< p < \infty$ and $1< q<q_\Phi$, there exists an equivalent Young function $\Psi$ with $p < p_\Psi < \infty$ and $1<q_\Psi < q$. This type…

This paper aims to develop basic theory for the dual Orlicz $L_{\phi}$ affine and geominimal surface areas for star bodies, which belong to the recent dual Orlicz-Brunn-Minkowski theory for star bodies. Basic properties for these new affine…

One can define Fourier multipliers on a Banach function space by using the direct and inverse Fourier transforms on $L^2(\mathbb{R}^n)$ or by using the direct Fourier transform on $S(\mathbb{R}^n)$ and the inverse one on $S'(\mathbb{R}^n)$.…