Displaying similar documents to “Musielak-Orlicz-Sobolev spaces with zero boundary values on metric measure spaces”

Musielak-Orlicz-Sobolev spaces on metric measure spaces

Takao Ohno, Tetsu Shimomura (2015)

Czechoslovak Mathematical Journal

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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...

Riesz potentials and Sobolev-type inequalities in Orlicz-Morrey spaces of an integral form

Takao Ohno, Tetsu Shimomura (2023)

Czechoslovak Mathematical Journal

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Our aim is to give Sobolev-type inequalities for Riesz potentials of functions in Orlicz-Morrey spaces of an integral form over non-doubling metric measure spaces as an extension of T. Ohno, T. Shimomura (2022). Our results are new even for the doubling metric measure spaces.

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.

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.

Remarks on the spaces of differentiable multifunctions

Andrzej Kasperski (2011)

Banach Center Publications

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In this paper we consider some spaces of differentiable multifunctions, in particular the generalized Orlicz-Sobolev spaces of multifunctions, we study completeness of them, and give some theorems.

On the continuity of Bessel potentials in Orlicz spaces.

N. Aïssaoui (1996)

Collectanea Mathematica

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It is shown that Bessel capacities in reflexive Orlicz spaces are non increasing under orthogonal projection of sets. This is used to get a continuity of potentials on some subspaces. The obtained results generalize those of Meyers and Reshetnyak in the case of Lebesgue classes.