We characterize the uniform non-squareness and the property of Besicovitch-Orlicz spaces of almost periodic functions equipped with Orlicz norm.
We consider uniformly non- almost periodic functions. It is shown that this property is equivalent to the reflexivity of this space.
We investigate which points in the unit sphere of the Besicovitch--Orlicz space of almost periodic functions, equipped with the Luxemburg norm, are extreme points. Sufficient conditions for the strict convexity of this space are also given.
In [6], the classical Riesz representation theorem is extended to the class of Besicovitch space of almost periodic functions a.p., . 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 a.p., where is an Orlicz function.
We revisit the concept of Stepanov--Orlicz almost periodic functions introduced by Hillmann in terms of Bochner transform. Some structural properties of these functions are investigated. A particular attention is paid to the Nemytskii operator between spaces of Stepanov--Orlicz almost periodic functions. Finally, we establish an existence and uniqueness result of Bohr almost periodic mild solution to a class of semilinear evolution equations with Stepanov--Orlicz almost periodic forcing term.
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