Approximation by means of Fourier trigonometric series in Morrey spaces

Abstract

In the present work we investigate the approximation of the functions by Ce-saro, Zygmund and Abel-Poisson means of Fourier series in Morrey spaces L p,λ ( T ) , 0 < λ ≤ 2 ,1 < p < ∞ in the terms of the modulus of continuity. These results applied to the estimates of approximation of Cesaro, Zygmund and Abel sums of Faber series in the Morrey-Smirnov classes E p,λ ( G ) , 0 < λ ≤ 2 and 1 < p < ∞ defined in the domains with Dini-smooth boundary of the complex plane.