Traces of Besov, Triebel-Lizorkin and Sobolev Spaces on Metric Spaces

Eero Saksman; Tomás Soto

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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].

Gelfand and Kolmogorov numbers of embedding of radial Besov and Sobolev spaces

Alicja Gąsiorowska (2011)

Banach Center Publications

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We prove asymptotic formulas for the behavior of Gelfand and Kolmogorov numbers of Sobolev embeddings between Besov and Triebel-Lizorkin spaces of radial distributions. Our method works also for Weyl numbers.

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.

The sharp Sobolev inequality in quantitative form

Andrea Cianchi, Nicola Fusco, F. Maggi, A. Pratelli (2009)

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Strokes of the biography of A. D. Alexandrov.

Kutateladze, S.S. (2001)

Vladikavkazskiĭ Matematicheskiĭ Zhurnal

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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.

Fifty years of Siberian Mathematical Journal.

Ershov, Yu.L., Kutateladze, S.S. (2009)

Sibirskij Matematicheskij Zhurnal

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Some remarks on relative diameters

V. M. Tikhomirov (1989)

Banach Center Publications

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On the Sobolev spaces I.

Crăciunaş, Petru Teodor (1996)

General Mathematics

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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.

On the intersection of Sobolev spaces

A. Benedek, R. Panzone (1990)

Colloquium Mathematicae

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A look on some results about Camassa–Holm type equations

Igor Leite Freire (2021)

Communications in Mathematics

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We present an overview of some contributions of the author regarding Camassa--Holm type equations. We show that an equation unifying both Camassa--Holm and Novikov equations can be derived using the invariance under certain suitable scaling, conservation of the Sobolev norm and existence of peakon solutions. Qualitative analysis of the two-peakon dynamics is given.

On the solvability of a multidimensional version of the Goursat problem for a second order hyperbolic equation with characteristic degeneration.

Kharibegashvili, Sergo (1997)

Memoirs on Differential Equations and Mathematical Physics

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Differentiability from the representation formula and the Sobolev-Poincaré inequality

Valentino Magnani (2005)

Studia Mathematica

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In the geometries of stratified groups, we provide differentiability theorems for both functions of bounded variation and Sobolev functions. Proofs are based on a systematic application of the Sobolev-Poincaré inequality and the so-called representation formula.

Addendum to the paper "On isomorphisms of anisotropic Sobolev spaces with "classical Banach spaces" and a Sobolev type embedding theorem"

A. Pełczyński, K. Senator (1986)

Studia Mathematica

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Metric characterizations of hyperbolic and Euclidean spaces

J. E. Valentine, S. G. Wayment (1972)

Colloquium Mathematicae

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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.

Sobolev-type spaces from generalized Poincaré inequalities

Toni Heikkinen, Pekka Koskela, Heli Tuominen (2007)

Studia Mathematica

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We define a Sobolev space by means of a generalized Poincaré inequality and relate it to a corresponding space based on upper gradients.

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.

Weighted Sobolev spaces and capacity.

Kilpeläinen, Tero (1994)

Annales Academiae Scientiarum Fennicae. Series A I. Mathematica

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Fifty years of the Siberian Division of the Russian Academy of Sciences.

Ershov, Yu.L., Kutateladze, S.S., Tajmanov, I.A. (2007)

Sibirskij Matematicheskij Zhurnal

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