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.
Michał Kisielewicz (1975)
Annales Polonici Mathematici
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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].
Lech Maligranda, Witold Wnuk (2004)
Banach Center Publications
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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.
Hudzik, H. (1981)
Portugaliae mathematica
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Małgorzata Doman (1991)
Commentationes Mathematicae Universitatis Carolinae
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We give necessary and sufficient conditions for weak uniform rotundity of Musielak–Orlicz spaces with the Luxemburg norm. The result is a generalization of a theorem by Kami’nska and Kurc.