Approximation of periodic functions of many variables by functions of smaller number of variables in Orlicz metric spaces - Babich, Yu. A.; Michaylova, T. F. (Ukrains’kyi Matematychnyi Zhurnal, 2018)
For periodic functions of many variables, the method of their approximation is offered in the Orlicz spaces $L_{φ} (T^m)$. 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 investigatedfor these approximations in terms of the mixed module of continuity.