Abstract
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.
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