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1
Content available remote On the strict convexity of Besicovitch-Musielak-Orlicz spaces of almost periodic functions equipped with the Orlicz norm
Daoui A., Morsli M., Smaali M.
Commentationes Mathematicae
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2013
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Vol. 53, No. 2
101--111
EN
We characterize the strict convexity of Besicovitch-Musielak-Orlicz spaces of almost periodic functions, when it is equipped with the Orlicz norm. It is shown that this property is equivalent to the strict convexity of the Musielak-Orlicz function generating the space.
2
Content available remote Characterization of the uniform convexity of the Besicovitch-Musielak-Orlicz spaces of almost periodic functions
Morsli M., Smaali M.
Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae
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2006
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Vol. 46, [Z] 2
215-231
EN
We introduce the new class of Besicovitch-Musielak-Orlicz spaces of almost periodic functions B'a.p..The uniform convexity of this space is characterized in terms of it’s generating functional [fi]
3
Content available remote Uniformly non-[formula] Besicovitch-Orlicz space of almost periodic functions
Morsli M., Boulahia F.
Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae
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2005
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Vol. 45, [Z] 1
25--34
EN
We consider uniformly non-[formula] property of the Besicovitch-Orlicz space of almost periodic functions. It is shownthat this property is equivalent to the reflexivity of this space.
4
Content available remote Characterization of the k-convexity property in the Besicovitch-Orlicz space of almost periodic functions
Bedouhene F., Morsli M.
Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae
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2005
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Vol. 45, [Z] 1
13--23
EN
In the present paper, we give criteria for the k-convexity of the Besicovitch-Orlicz space of almost periodic functions. Namely,it is shown that k-convexity is equivalent to strict convexity and reflexivity of this space in the case of Luxemburg norm.
5
Content available remote On uniform convexity and modular approximation in the Weyl-Orlicz spaces
Bedouhene F., Morsli M.
Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae
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2001
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[Z] 41
25-39
EN
Uniform convexity is well characterized in Orlicz spaces for both the Luxemburg and Orlicz norms [2], [3], [4] and in Besicovitch-Orlicz spaces of almost periodic functions for the Luxemburg norm [7]. The existence problem of the projection operator on closed convex subsets was considered in [5] in the case of Orlicz spaces, and in [8] in the case of Besicovitch-Orlicz space of almost periodic functions. In this paper we characterize the uniform convexity property in the Weyl-Orlicz spaces of almost periodic functions (W^a.p.) under the Luxemburg norm. Next this result is used to state the existence of the projection operator on complete convex subsets of W^a.p.
6
Content available remote On strict convexity of the Weyl-Orlicz space of almost periodic functions
Bedouhene F., Morsli M.
Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae
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2000
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[Z] 40
33-47
EN
Abstract. In [2], T.R. Hillmann investigated some structural and topo-logical properties of the Besicovitch-Orlicz space (and others like as the Stepanoff and Weyl-Orlicz spaces) and his subspaces of almost periodic functions. In [3], we characterized the strict and uniform convexity of this space. In this paper, the strict convexity property is characterized in the Weyl-Orlicz space of almost periodic functions
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