On the Euler-Lagrange inequality of a convex variational integral in Orlicz spaces
Ari Lehtonen (1987)
Banach Center Publications
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Ari Lehtonen (1987)
Banach Center Publications
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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.
Zhikov, V.V. (2004)
Journal of Mathematical Sciences (New York)
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Jürgen Appell (2004)
Banach Center Publications
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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.
Paweł Kolwicz (2005)
Banach Center Publications
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We prove that the Musielak-Orlicz sequence space with the Orlicz norm has property (β) iff it is reflexive. It is a generalization and essential extension of the respective results from [3] and [5]. Moreover, taking an arbitrary Musielak-Orlicz function instead of an N-function we develop new methods and techniques of proof and we consider a wider class of spaces than in [3] and [5].
Michał Kisielewicz (1975)
Annales Polonici Mathematici
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Lech Maligranda, Witold Wnuk (2004)
Banach Center Publications
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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.
Tao Zhang (2003)
Annales Polonici Mathematici
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Estimation of the Jung constants of Orlicz sequence spaces equipped with either the Luxemburg norm or the Orlicz norm is given. The exact values of the Jung constants of a class of reflexive Orlicz sequence spaces are found by using new quantitative indices for 𝓝-functions.
Jimin Zheng, Lihuan Sun, Yun'an Cui (2008)
Banach Center Publications
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In this paper, the criteria of strong roughness, roughness and pointwise roughness of Orlicz norm and Luxemburg norm on Musielak-Orlicz function spaces are obtained.
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.
Ting Fu Wang, Zhong Rui Shi, Quan Di Wang (1993)
Collectanea Mathematica
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For Orlicz spaces with Orlicz norm, a criterion of W*UR point is given, and previous results about UR points and WUR points are amended.
Aïssaoui, Noureddine (2004)
Southwest Journal of Pure and Applied Mathematics [electronic only]
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Hudzik, H. (1981)
Portugaliae mathematica
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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...