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1 Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae

1 2001

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On uniform convexity and modular approximation in the Weyl-Orlicz spaces

Bedouhene F., Morsli M.

Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae

2001

[Z] 41

25-39

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.