Approximation by De La Vallée Poussin means in weighted generalized grand Smirnov classes

Abstract

Let G be a simple connected domain on complex plane such that Γ := ∂G where Γ is a Carleson curve. In this work, we investigate the rate of approximation by De La Vall´ee Poussin mean constructed via p − ε Faber series in the proper subclass of weighted generalized grand Smirnov classes Ep),θω (G), 1 < p < ∞ where the ω satisfying Muckenhoupt’s condition.