Estimates of the Approximations by Zygmund Sums in Morrey-Smirnov Classes of Analytic Functions

Abstract

In the present work, we investigate the approximation of the functions by Zygmund means of Fourier series in Morrey spaces L-p,L-lambda (T), 0 < lambda <= 2, 1 < p < infinity in the terms of the modulus of smoothness. The obtained results are applied to estimate the approximation of functions by Zygmund sums of Faber series in Morrey-Smirnov classes defined on simply connected domains of the complex plane. In this case, the obtained estimation depends on the sequence of the best approximation in Morrey-Smirnov classes.