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

Alireza Ranjbar-Motlagh

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Displaying similar documents to “An embedding theorem for Sobolev type functions with gradients in a Lorentz space”

Musielak-Orlicz-Sobolev spaces on metric measure spaces

Takao Ohno, Tetsu Shimomura (2015)

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Our aim in this paper is to study Musielak-Orlicz-Sobolev spaces on metric measure spaces. We consider a Hajłasz-type condition and a Newtonian condition. We prove that Lipschitz continuous functions are dense, as well as other basic properties. We study the relationship between these spaces, and discuss the Lebesgue point theorem in these spaces. We also deal with the boundedness of the Hardy-Littlewood maximal operator on Musielak-Orlicz spaces. As an application of the boundedness...

Musielak-Orlicz-Sobolev spaces with zero boundary values on metric measure spaces

Takao Ohno, Tetsu Shimomura (2016)

Czechoslovak Mathematical Journal

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We define and study Musielak-Orlicz-Sobolev spaces with zero boundary values on any metric space endowed with a Borel regular measure. We extend many classical results, including completeness, lattice properties and removable sets, to Musielak-Orlicz-Sobolev spaces on metric measure spaces. We give sufficient conditions which guarantee that a Sobolev function can be approximated by Lipschitz continuous functions vanishing outside an open set. These conditions are based on Hardy type...

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Andrea Cianchi (1996)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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Orlicz-Sobolev spaces with zero boundary values on metric spaces.

Aïssaoui, Noureddine (2004)

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Fine behavior of functions whose gradients are in an Orlicz space

Jan Malý, David Swanson, William P. Ziemer (2009)

Studia Mathematica

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For functions whose derivatives belong to an Orlicz space, we develop their "fine" properties as a generalization of the treatment found in [MZ] for Sobolev functions. Of particular importance is Theorem 8.8, which is used in the development in [MSZ] of the coarea formula for such functions.

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Pierre-A. Vuillermot (1987/88)

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Zhikov, V.V. (2004)

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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.

Strokes of the biography of A. D. Alexandrov.

Kutateladze, S.S. (2001)

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Extrapolation of Sobolev imbeddings.

M. Krbec (1997)

Collectanea Mathematica

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We survey recent results on limiting imbeddings [sic] of Sobolev spaces, particularly, those concerning weakening of assumptions on integrability of derivatives, considering spaces with dominating mixed derivatives and the case of weighted spaces.