Approximation of periodic functions of many variables by functions of smaller number of variables in Orlicz metric spaces

Abstract

For periodic functions of many variables, the method of their approximation is offered in the Orlicz spaces $L_{\varphi} (T^m)$. In this method, the functions are approximated by the sums of functions of smaller number of variables, each of which is piecewiswe-constant in one of variables for fixed values of the other variables. A Jackson-type inequality is investigated for these approximations in terms of the mixed module of continuity.