Approximation in weighted generalized grand Smirnov classes

Abstract

Let G be a finite simple connected domain in the complex plane C, bounded by a Carleson curve Γ := ∂G. In this work the direct and inverse theorems of approximation theory by the algebraic polynomials in the weighted generalized grand Smirnov classes ϵp ),θ(G,ω) and Ep),θ(G - ,ω), 1 < p < ∞, 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.