On exact estimates of the order of approximation of functions of several variables in the anisotropic Lorentz--Zygmund space - Gabdolla Akishev (Hilbert Journal of Mathematical Analysis, 2025)
In this paper we consider $L_{\overline{p}, \overlineα, \overline{τ}}^{*}(\mathbb{T}^{m})$ anisotropic Lorentz-Zyg\-mu\-nd space $ 2π$ of periodic functions of $m$ variables and Nikol'skii--Besov's class $S_{\overline{p}, \overlineα, \overline{τ}, \bar{θ}}^{\bar r}B$. 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.