Related papers: Sobolev spaces and averaging I

We provide new characterizations of Sobolev ad BV spaces in doubling and Poincare metric spaces in the spirit of the Bourgain-Brezis-Mironescu and Nguyen limit formulas holding in domains of R^N.

We firstly describe a maximal inequality for dual Sobolev spaces W^{-1,p}. This one corresponds to a "Sobolev version" of usual properties of the Hardy-Littlewood maximal operator in Lebesgue spaces. Even in the euclidean space, this one…

The properties of the spaces of Sugeno integrable functions are quite different from those of the ordinary spaces of Lebesgue integrable functions. The purpose of the paper is to further advance our study of the Sugeno-Lorentz spaces, in…

On a general open set of the euclidean space, we study the relation between the embedding of the homogeneous Sobolev space $\mathcal{D}^{1,p}_0$ into $L^q$ and the summability properties of the distance function. We prove that in the…

Properties of first-order Sobolev-type spaces on abstract metric measure spaces, so-called Newtonian spaces, based on quasi-Banach function lattices are investigated. The set of all weak upper gradients of a Newtonian function is of…

This paper introduces Sobolev spaces over Gelfand pairs in the framework of hypergroups. The Sobolev spaces in question are constructed from the Fourier transform on hypergroup Gelfand pairs. Mainly, the paper focuses on the investigation…

In this paper, the authors establish new characterizations of the recently introduced Besov-type spaces $\dot{B}^{s,\tau}_{p,q}({\mathbb R}^n)$ and Triebel-Lizorkin-type spaces $\dot{F}^{s,\tau}_{p,q}({\mathbb R}^n)$ with $p\in (0,\infty]$,…

We extend in this article the classical imbedding theorems for fractional Lebesgue-Sobolev's spaces into the so-called Grand Lebesgue spaces, with sharp constant evaluation.

The subject is traces of Sobolev spaces with mixed Lebesgue norms on Euclidean space. Specifically, restrictions to the hyperplanes given by the first and last coordinates are applied to functions belonging to quasi-homogeneous, mixed-norm…

In this paper, we investigate the convergence of the Bochner-Riesz means on some Sobolev type spaces including $L^p$-Sobolev spaces $(p\geq 1)$ and $H^q$-Sobolev spaces $(0<q<1)$. The relation between the smoothness imposed on functions and…

We define Euler-Hilbert-Sobolev spaces and obtain embedding results on homogeneous groups using Euler operators, which are homogeneous differential operators of order zero. Sharp remainder terms of $L^{p}$ and weighted Sobolev type and…

We study one-dimensional linear hyperbolic systems with $L^{\infty}$-coefficients subjected to periodic conditions in time and reflection boundary conditions in space. We derive a priori estimates and give an operator representation of…

The structure of non-compactness of optimal Sobolev embeddings of $m$-th order into the class of Lebesgue spaces and into that of all rearrangement-invariant function spaces is quantitatively studied. Sharp two-sided estimates of Bernstein…

This work focuses on an improved fractional Sobolev inequality with a remainder term involving the Hardy-Littlewood-Sobolev inequality which has been proved recently. By extending a recent result on the standard Laplacian to the fractional…

A Bourgain--Brezis--Mironescu-type theorem for fractional Sobolev spaces with variable exponents is established for sufficiently regular functions. We prove, however, that a limiting embedding theorem for these spaces fails to hold in…

Reparametrization invariant Sobolev metrics on spaces of regular curves have been shown to be of importance in the field of mathematical shape analysis. For practical applications, one usually discretizes the space of smooth curves and…

We consider the equivalence of some norms in Sobolev spaces on bounded domains of the d-dimensional real Euclidean space and also in Sobolev spaces on the boundaries of those domains.

We introduce Herz-Sobolev spaces, which unify and generalize the classical Sobolev spaces. We will give a proof of the Sobolev-type embedding for these function spaces. All these results generalize the classical results on Sobolev spaces.…

We extend the classical Hardy-Sobolev-Poincare-Wirtinger inequalities from the ordinary Lebesgue-Riesz spaces into the Grand Lebesgue ones, with exact constants evaluation.

After proving the equivalence of the Bessel $K$-functional and the corresponding spherical modulus of smoothness we define fractional Bessel-Sobolev spaces. As an analog of the classical one the imbedding relation of fractional…