APPROXIMATION IN WEIGHTED GENERALIZED GRAND SMIRNOV CLASSES

摘要

Let G be a finite simple connected domain in the complex plane C, bounded by a Carleson curve Gamma := partial derivative G. In this work the direct and inverse theorems of approximation theory by the algebraic polynomials in the weighted generalized grand Smirnov classes epsilon(p),theta(G,omega)) and epsilon(p),theta(G-,omega)), 1 p infinity, in the term of the rth, r = 1, 2, ... , mean modulus of smoothness are proved. As a corollary the constructive characterizations of the weighted generalized grand Lipschitz classes are obtained.