Related papers: Optimal domain spaces in Orlicz-Sobolev embeddings
In this article we first establish a complete characterization of Hardy's inequalities in $\mathbb{R}^n$ involving distances to different codimension subspaces. In particular the corresponding potentials have strong interior singularities.…
A full characterization of the boundedness of Laplace--Carleson embeddings on $L^\infty$ is provided, in terms of the Carleson intensity of the respective measure and of a suitable weighted Berezin transform of the measure. Moreover,…
We associate a sequence of variational eigenvalues to any Radon measure on a compact Riemannian manifold. For particular choices of measures, we recover the Laplace, Steklov and other classical eigenvalue problems. In the first part of the…
There are investigated problems connected with local and boundary properties of Orlicz--Sobolev classes of finite distortion which are actively studied last time. It is showed that, a locally uniform limit of local homeomorphisms of…
We study problems related to continuous boundary extension of mappings of Orlicz-Sobolev classes in terms of prime ends. The results we obtain concern the case when the mappings are open, discrete, but not closed (not preserving the…
Given a monotone convex function on the space of essentially bounded random variables with the Lebesgue property (order continuity), we consider its extension preserving the Lebesgue property to as big solid vector space of random variables…
We prove the existence of an open set minimizing the first Dirichlet eigenvalue of an elliptic operator with bounded, measurable coefficients, over all open sets of a given measure. Our proof is based on a free boundary approach: we…
In this paper, we find necessary and sufficient conditions for the boundedness of fractional maximal operator $M_{\alpha}$ on Orlicz spaces. As an application of this results we consider the boundedness of fractional maximal commutator…
We show that a domain is an extension domain for a Haj\l asz-Besov or for a Haj\l asz-Triebel-Lizorkin space if and only if it satisfies a measure density condition. We use a modification of the Whitney extension where integral averages are…
In this paper we introduce a new technique to prove the existence of closed subspaces of maximal dimension inside sets of topological vector sequence spaces. The results we prove cover some sequence spaces not studied before in the context…
In this paper, we investigate the relation between Sobolev-type embeddings of Haj{\l}asz-Besov spaces (and also Haj{\l}asz-Triebel-Lizorkin spaces) defined on a metric measure space $(X,d,\mu)$ and lower bound for the measure $\mu.$ We…
Due to the growing interest in embeddings of space-time in higher-dimensional spaces we consider a specific type of embedding. After proving an inequality between intrinsically defined curvature invariants and the squared mean curvature, we…
We prove a general theorem showing that local good-$\lambda$ inequalities imply bounds in certain variable Orlicz spaces. We use this to prove results about variable Orlicz Hardy spaces in the unit disc.
The continuity of the Nemytskii operator between Orlicz-Sobolev spaces is investigated. Natural Orlicz-Sobolev versions of classical results for standard Sobolev are established. The results presented not only extend the latter, but also…
We investigate distortion estimates for mappings at boundary points of a domain. We consider mappings of the Sobolev and Orlicz-Sobolev classes and some other classes of mappings that do not preserve the boundary of a domain. For above…
We construct whole-space extensions of functions in a fractional Sobolev space of order $s\in (0,1)$ and integrability $p\in (0,\infty)$ on an open set $O$ which vanish in a suitable sense on a portion $D$ of the boundary $\partial O$ of…
Let X and Y be two infinite-dimensional Banach spaces. If X is crudely finitely representable in every finite-codimensional subspace of Y, then any proper subset of X almost bi-Lipschitz embeds into Y, in a sense quite close to that of F.…
In this paper, we study the critical Sobolev embeddings $W^{1,p(x)}(\Omega)\subset L^{p^*(x)}(\Omega)$ for variable exponent Sobolev spaces from the point of view of the $\Gamma$-convergence. More precisely we determine the $\Gamma$-limit…
This paper is devoted to giving definitions of Besov spaces on an arbitrary open set of $\mathbb R^n$ via the spectral theorem for the Schr\"odinger operator with the Dirichlet boundary condition. The crucial point is to introduce some test…
We investigate the dependence of optimal constants in Poincar\'e- Sobolev inequalities of planar domains on the region where the Dirichlet condition is imposed. More precisely, we look for the best Dirichlet regions, among closed and…