Displaying similar documents to “On modular approximation property in the Besicovitch-Orlicz space of almost periodic functions”

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

Fazia Bedouhene, Mohamed Morsli, Mannal Smaali (2010)

Commentationes Mathematicae Universitatis Carolinae

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The paper is concerned with the characterization and comparison of some local geometric properties of the Besicovitch-Orlicz space of almost periodic functions. Namely, it is shown that local uniform convexity, H -property and strict convexity are all equivalent. In our approach, we first prove some metric type properties for the modular function associated to our space. These are then used to prove our main equivalence result.

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.