Certain properties of generalized Orlicz spaces.
Jain, Pankaj, Upreti, Priti (2009)
JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]
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Jain, Pankaj, Upreti, Priti (2009)
JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]
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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.
Andrea Cianchi (1996)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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Zhikov, V.V. (2004)
Journal of Mathematical Sciences (New York)
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Aïssaoui, Noureddine (2004)
Southwest Journal of Pure and Applied Mathematics [electronic only]
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Jürgen Appell (2004)
Banach Center Publications
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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...
Ha Huy Bang, Nguyen Van Hoang, Vu Nhat Huy (2011)
Bulletin of the Polish Academy of Sciences. Mathematics
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We investigate best constants for inequalities between the Orlicz norm and Luxemburg norm in Orlicz spaces.
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.
Lech Maligranda, Witold Wnuk (2004)
Banach Center Publications
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Zenon Zbąszyniak (1994)
Commentationes Mathematicae Universitatis Carolinae
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There is given a criterion for an arbitrary element from the unit sphere of Musielak-Orlicz function space equipped with the Luxemburg norm to be a point of smoothness. Next, as a corollary, a criterion of smoothness of these spaces is given.