On approximation of functions, conjugate to the functions of several variables belonging to weighted Lipschitz and Zygmund classes

Abstract

In the present paper, we introduce a new weighted Lipschitz class W(Lp(TN), ξ1(s1), . . . , ξN(sN)) and Zygmund class Z(Lp(TN), ξ1(s1), . . . , ξN(sN)) for N ∈ N, which generalizes the classes given in [7, 11]. We prove two theorems about
 the degree (error) of approximation of functions, conjugate to the N-variable functions (2π-periodic in each variable) belonging to these classes using the N-multiple matrix means of their N-multiple conjugate Fourier series. We improve the results of Móricz and Rhoades [6] and Móricz and Shi [7], which are given in the form of corollaries.