Estimates of the best approximations of the functions of the Nikol'skii-Besov class in the generalized space of Lorentz

摘要

In this paper, we consider the generalized Lorentz space of periodic functions of several variables and the Nikol'skii-Besov space of functions. The article establishes a sufficient condition for a function to belong from one generalized Lorentz space to another space in terms of the difference of the partial sums of the Fourier series of a given function. Exact in order estimates of the best approximation by trigonometric polynomials of functions of the Nikol'skii-Besov class are obtained.