On orders of approximation of the generalized Nikol'\''skii--Besov class in Lorentz spaces

Abstract

This paper considers the Lorentz space with mixed norm of periodic functions of many variables and of the generalized Nikol'\''skii--Besov classes. Estimates for the order of approximation of the generalized Nikol'\''skii--Besov classes by partial sums of Fourier'\''s series for multiple trigonometric system in Lorentz spaces with mixed norm are obtained.