Displaying similar documents to “On some equivalent geometric properties in the Besicovitch-Orlicz space of almost periodic functions with Luxemburg norm”

On some convexity properties in the Besicovitch-Musielak-Orlicz space of almost periodic functions with Luxemburg norm

Fazia Bedouhene, Amina Daoui, Hocine Kourat (2012)

Commentationes Mathematicae Universitatis Carolinae

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In this article, it is shown that geometrical properties such as local uniform convexity, mid point local uniform convexity, H-property and uniform convexity in every direction are equivalent in the Besicovitch-Musielak-Orlicz space of almost periodic functions ( B ˜ ϕ a . p . ) endowed with the Luxemburg norm.

Duality properties and Riesz representation theorem in Besicovitch-Musielak-Orlicz space of almost periodic functions

A. Daoui, Mohamed Morsli, M. Smaali (2012)

Commentationes Mathematicae Universitatis Carolinae

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This paper is an extension of the work done in [Morsli M., Bedouhene F., Boulahia F., Duality properties and Riesz representation theorem in the Besicovitch-Orlicz space of almost periodic functions, Comment. Math. Univ. Carolin. 43 (2002), no. 1, 103--117] to the Besicovitch-Musielak-Orlicz space of almost periodic functions. Necessary and sufficient conditions for the reflexivity of this space are given. A Riesz type ``duality representation theorem'' is also stated.

Duality properties and Riesz representation theorem in the Besicovitch-Orlicz space of almost periodic functions

Mohamed Morsli, Fazia Bedouhene, Fatiha Boulahia (2002)

Commentationes Mathematicae Universitatis Carolinae

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In [6], the classical Riesz representation theorem is extended to the class of Besicovitch space of almost periodic functions B q  a.p., q ∈ ] 1 , + ∞ [ . It is also shown that this space is reflexive. We shall consider here such results in the context of Orlicz spaces, namely in the class of Besicovitch-Orlicz space of almost periodic functions B φ  a.p., where φ is an Orlicz function.