Approximation by means of fourier trigonometric series in weighted orlicz spaces

Abstract

The order of approximation of Cesaro, Zygmund and Abel-Poisson means of Fourier trigonometric series were estimated by the modulus of continuity in reflexive weighted Orlicz spaces with Muckenhoupt weights. These results were applied to estimate the rate of approximation of Cesaro, Zygmund and Abel sums of Faber series in weighted Smirnov-Orlicz classes defined on simply connected domains of the complex plane.