Related papers: Non-separably valued Orlicz spaces, part I

We study the general measures of non-compactness defined on subsets of a dual Banach space, their associated derivations and their $\omega$-iterates. We introduce the notions of convexifiable and sublinear measure of non-compactness and…

We extend to the non separable setting many characterizations of the Banach spaces admitting an equivalent norm with the property $(\beta)$ of Rolewicz. These characterizations involve in particular the Szlenk index and asymptotically…

In this work, we establish some abstract results on the perspective of the fractional Musielak-Sobolev spaces, such as: uniform convexity, Radon-Riesz property with respect to the modular function, $(S_{+})$-property, Brezis-Lieb type Lemma…

An extension of Marcinkiewicz Interpolation Theorem, allowing intermediate spaces of Orlicz type, is proved. This generalization yields a necessary and sufficient condition so that every quasilinear operator, which maps the set, $S(X,\mu)$,…

Let $\varphi:\mathbb{R}^n\times[0,\,\infty) \rightarrow [0,\,\infty)$ satisfy that $\varphi(x,\,\cdot)$, for any given $x\in\mathbb{R}^n$, is an Orlicz function and $\varphi(\cdot\,,t)$ is a Muckenhoupt $A_\infty$ weight uniformly in…

Let $X$ be a real Banach space and let $Y \subseteq X^*$ be a linear subspace having the Orlicz-Thomas property, that is, for each $\sigma$-algebra $\Sigma$ and for each map $\nu:\Sigma\to X$, the countable additivity of the composition…

We provide a variety of results for (quasi)convex, law-invariant functionals defined on a general Orlicz space, which extend well-known results in the setting of bounded random variables. First, we show that Delbaen's representation of…

In this paper we are concerned with some abstract results regarding to fractional Orlicz-Sobolev spaces. Precisely, we ensure the compactness embedding for the weighted fractional Orlicz-Sobolev space into the Orlicz spaces, provided the…

Non-convex functions that yet satisfy a condition of uniform convexity for non-close points can arise in discrete constructions. We prove that this sort of discrete uniform convexity is inherited by the convex envelope, which is the key to…

Several local geometric properties of Orlicz space $L_\phi$ are presented for an increasing Orlicz function $\phi$ which is not necessarily convex, and thus $L_\phi$ does not need to be a Banach space. In addition to monotonicity of $\phi$…

In this paper, we obtain a minimax theorem by means of which, in turn, we prove the following result: Let $E$ be an infinite-dimensional reflexive real Banach space, $T:E\to E$ a non-zero compact linear operator, $\varphi:E\to {\bf R}$ a…

In the present paper we introduce a certain class of non commutative Orlicz spaces, associated with arbitrary faithful normal locally-finite weights on a semi-finite von Neumann algebra $M.$ We describe the dual spaces for such Orlicz…

We provide explicit formulas for the norm of bounded linear functionals on Orlicz-Lorentz function spaces $\Lambda_{\varphi,w}$ equipped with two standard Luxemburg and Orlicz norms. Any bounded linear functional is a sum of regular and…

In this paper, we study integral functionals defined on spaces of functions with values on general (non-separable) Banach spaces. We introduce a new class of integrands and multifunctions for which we obtain measurable selection results.…

In this paper, we introduce the notions of $\alpha$-quasicomplemented and totally $\alpha$-quasicomplemented subspaces and we established some results under these contexts. We show, for example, that if $X$ is a separable or reflexive…

A well-known open question is whether every countable collection of Lipschitz functions on a Banach space X with separable dual has a common point of Frechet differentiability. We show that the answer is positive for some…

This article introduces the notion of arithmetic Bohr radius for operator valued pluriharmonic functions on complete Reinhardt domains in $\mathbb{C}^n$. Using tools from local Banach space theory, we determine its asymptotic behavior in…

The paper concerns the investigation of nonconvex and nondifferentiable integral functionals on general Banach spaces, which may not be reflexive and/or separable. Considering two major subdifferentials of variational analysis, we derive…

In the article we generalize the Marcinkiewicz sampling theorem in the context of Orlicz spaces. We establish conditions under which sampling theorem holds in terms of restricted submultiplicativity and supermultiplicativity of an…

Using a nonlinear version of the well known Hardy-Littlewood inequalities, we derive new formulas for decreasing rearrangements of functions and sequences in the context of convex functions. We use these formulas for deducing several…