On the $k$-convexity of the Besicovitch–Orlicz space of almost periodic functions with the Orlicz norm
Volume 109 / 2007
Colloquium Mathematicum 109 (2007), 107-118
MSC: 46B20, 42A75.
DOI: 10.4064/cm109-1-9
Abstract
Boulahia and the present authors introduced the Orlicz norm in the class $B^{\phi }$-a.p. of Besicovitch–Orlicz almost periodic functions and gave several formulas for it; they also characterized the reflexivity of this space [Comment. Math. Univ. Carolin. 43 (2002)]. In the present paper, we consider the problem of $k$-convexity of $B^{\phi }$-a.p. with respect to the Orlicz norm; we give necessary and sufficient conditions in terms of strict convexity and reflexivity.
