ON THE BEST POLYNOMIAL APPROXIMATIONS OF FUNCTIONS OF MANY REAL VARIABLES FROM THE SOBOLEV SPACE WITH DERIVATIVES OF BOUNDED VARIATION

The paper is devoted to estimates of the best joint polynomial approximations in uniform and integral metrics on a given bounded convex domain of the functions of many real variables (FMRV) either with convex derivatives of a certain order or from the seminormalized Sobolev space with derivatives of a certain order of bounded variation.