APPROXIMATION OF PERIODIC FUNCTIONS OF MANY VARIABLES BY FUNCTIONS OF A SMALLER NUMBER OF VARIABLES IN ORLICZ METRIC SPACES

For periodic functions of many variables, we propose a method for their approximation in the Orlicz spaces L-phi(T-m). According to this method, the functions are approximated by the sums of functions of smaller number of variables each of which is piecewise-constant in one variable for fixed values of the other variables. A Jackson-type inequality is analyzed for these approximations in terms of the mixed module of continuity.