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On the strict convexity of Besicovitch-Musielak-Orlicz spaces of almost periodic functions equipped with the Orlicz norm

A. Daoui; M. Morsli; M. Smaali — 2013

Commentationes Mathematicae

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.

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

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.

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On the strict convexity of Besicovitch-Musielak-Orlicz spaces of almost periodic functions equipped with the Orlicz norm

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