Another extension of Orlicz--Sobolev spaces to metric spaces.
Aïssaoui, Noureddine (2004)
Abstract and Applied Analysis
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Displaying similar documents to “Strongly nonlinear potential theory on metric spaces.”
Another extension of Orlicz--Sobolev spaces to metric spaces.
On the uniformly normal structure of Orlicz spaces with Orlicz norm
Ting Fu Wang, Zhong Rui Shi (1993)
Commentationes Mathematicae Universitatis Carolinae
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We prove that in Orlicz spaces endowed with Orlicz norm the uniformly normal structure is equivalent to the reflexivity.
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...
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...
Continuity properties of functions from Orlicz-Sobolev spaces and embedding theorems
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)
Southwest Journal of Pure and Applied Mathematics [electronic only]
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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.