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.

arXiv commentarXiv admin note: substantial text overlap with arXiv:2105.06796

References in corpus (3)

• Direct and inverse approximation theorems of functions in the Orlicz type spaces S_M
• Direct and inverse theorems of approximation of functions in weighted Orlicz type spaces with variable exponent
• Direct and inverse theorems on the approximation of almost periodic functions in Besicovitch-Stepanets spaces

Cited by in corpus (1)

• Actual problems of the approximation theory in metrics of discrete spaces on sets of summable periodic and almost periodic functions