On orders of approximation of the generalized Nikol’skiу-Besov class in Lorentz spaces

Abstract

In this paper Lorentz space is considered with mixed norm. Definition of the generalized Nikol’skiy-Besov classes is given. The main results of the paper are the estimates of the order of approximation of functions of the generalized Nikol’skiy-Besov class by partial sums of multiply series Fourier constructed with harmonics from the hyperbolic cross.