Approximation of functions of weighted lebesgue and smirnov spaces

Abstract

In this work we investigate the inverse approximation problems in the Lebesgue and Smirnov spaces with weights satisfying the so-called Mucken-houpt's A p condition in terms of the α-th mean modulus of smoothness, α > 0. We obtain a converse theorem of trigonometric approximation in the weighted Lebesgue spaces and obtain some converse theorems of algebraic polynomial approximation in the weighted Smirnov spaces.