Displaying similar documents to “Traces of Besov, Triebel-Lizorkin and Sobolev Spaces on Metric Spaces”

Hölder quasicontinuity of Sobolev functions on metric spaces.

Piotr Hajlasz, Juha Kinnunen (1998)

Revista Matemática Iberoamericana

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We prove that every Sobolev function defined on a metric space coincides with a Hölder continuous function outside a set of small Hausdorff content or capacity. Moreover, the Hölder continuous function can be chosen so that it approximates the given function in the Sobolev norm. This is a generalization of a result of Malý [Ma1] to the Sobolev spaces on metric spaces [H1].

Variable Sobolev capacity and the assumptions on the exponent

Petteri Harjulehto, Peter Hästö, Mika Koskenoja, Susanna Varonen (2005)

Banach Center Publications

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In a recent article the authors showed that it is possible to define a Sobolev capacity in variable exponent Sobolev space. However, this set function was shown to be a Choquet capacity only under certain assumptions on the variable exponent. In this article we relax these assumptions.

An embedding theorem for Sobolev type functions with gradients in a Lorentz space

Alireza Ranjbar-Motlagh (2009)

Studia Mathematica

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The purpose of this paper is to prove an embedding theorem for Sobolev type functions whose gradients are in a Lorentz space, in the framework of abstract metric-measure spaces. We then apply this theorem to prove absolute continuity and differentiability of such functions.

Brézis-Gallouët-Wainger type inequality for Besov-Morrey spaces

Yoshihiro Sawano (2010)

Studia Mathematica

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The aim of the present paper is to obtain an inequality of Brézis-Gallouët-Wainger type for Besov-Morrey spaces. We investigate these spaces in a self-contained manner. Also, we verify that our result is sharp.

Dimension-invariant Sobolev imbeddings

Miroslav Krbec, Hans-Jürgen Schmeisser (2011)

Banach Center Publications

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We survey recent dimension-invariant imbedding theorems for Sobolev spaces.

The Besov capacity in metric spaces

Juho Nuutinen (2016)

Annales Polonici Mathematici

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We study a capacity theory based on a definition of Hajłasz-Besov functions. We prove several properties of this capacity in the general setting of a metric space equipped with a doubling measure. The main results of the paper are lower bound and upper bound estimates for the capacity in terms of a modified Netrusov-Hausdorff content. Important tools are γ-medians, for which we also prove a new version of a Poincaré type inequality.

Hessian determinants as elements of dual Sobolev spaces

Teresa Radice (2014)

Studia Mathematica

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In this short note we present new integral formulas for the Hessian determinant. We use them for new definitions of Hessian under minimal regularity assumptions. The Hessian becomes a continuous linear functional on a Sobolev space.

Poincaré inequality and Hajłasz-Sobolev spaces on nested fractals

Katarzyna Pietruska-Pałuba, Andrzej Stós (2013)

Studia Mathematica

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Given a nondegenerate harmonic structure, we prove a Poincaré-type inequality for functions in the domain of the Dirichlet form on nested fractals. We then study the Hajłasz-Sobolev spaces on nested fractals. In particular, we describe how the "weak"-type gradient on nested fractals relates to the upper gradient defined in the context of general metric spaces.

Mixed norms and Sobolev type inequalities

V. I. Kolyada (2006)

Banach Center Publications

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We study mixed norm spaces that arise in connection with embeddings of Sobolev and Besov spaces. We prove Sobolev type inequalities in terms of these mixed norms. Applying these results, we obtain optimal constants in embedding theorems for anisotropic Besov spaces. This gives an extension of the estimate proved by Bourgain, Brezis and Mironescu for isotropic Besov spaces.