The importance of being Orlicz
Jürgen Appell (2004)
Banach Center Publications
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Jürgen Appell (2004)
Banach Center Publications
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Randrianantoanina, Beata (2004)
Abstract and Applied Analysis
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César Ruiz (1990)
Acta Universitatis Carolinae. Mathematica et Physica
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Henryk Hudzik, Zenon Zbaszyniak (1997)
Collectanea Mathematica
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A formula for the distance of an arbitrary element x in Musielak-Orlicz space L^Phi from the subspace E^Phi of order continuous elements is given for both (the Luxemburg and the Orlicz) norms. A formula for the norm in the dual space of L^Phi is given for any of these two norms. Criteria for smooth points and smoothness in L^Phi and E^Phi equipped with the Orlicz norm are presented.
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.
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.
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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Hudzik, H. (1981)
Portugaliae mathematica
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Lech Maligranda, Witold Wnuk (2004)
Banach Center Publications
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