Direct and inverse approximation theorems in the Besicovitch-Museilak-Orlicz spaces of almost periodic functions

Abstract: In terms of the best approximations of functions and generalized moduli of smoothness, direct and inverse approximation theorems are proved for Besicovitch almost periodic functions whose Fourier exponent sequences have a single limit point in infinity and their Orlicz norms are finite. Special attention is paid to the study of cases when the constants in these theorems are unimprovable.