On exact estimates of the order of approximation of functions of several variables in the anisotropic Lorentz-Zygmund space

Abstract

In this paper we consider $L_{\overline{p},\overline{\alpha },\overline{\tau }}^{\ast }({\mathbb{T}}^m)$ anisotropic Lorentz-Zyg\-mu\-nd space $2\pi$ of periodic functions of $m$ variables and Nikol'skii--Besov's class $S_{\overline{p},\overline{\alpha },\overline{\tau },\bar{\theta }}^{\bar{r}}B$. In this paper, we establish order-sharp estimates of the best approximation by trigonometric polynomials with harmonic numbers from the step hyperbolic cross of functions from the Nikol'skii - Besov class in the norm of the anisotropic Lorentz-Zygmund space.

arXiv comment20 pages