We introduce the new class of Besicovitch-Musielak-Orlicz spaces of almost periodic functions . The uniform convexity of this space is characterized in terms of it’s generating functional .
We introduce the new class of Besicovitch-Musielak-Orlicz almost periodic functions and consider its strict convexity with respect to the Luxemburg norm.
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, -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.
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