Displaying similar documents to “Duality properties and Riesz representation theorem in Besicovitch-Musielak-Orlicz space of almost periodic functions”

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.

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.