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Gabdolla Akishev
Kazakhstan Branch of Lomonosov Moscow State University
Chemistry Control & Systems Engineering Engineering Mathematics Physics

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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 Vol. 4 No. 1 (2025): Hilbert J. Math. Anal.
Publisher : KOMUNITAS Analisis Matematika INDONESIA

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.62918/hjma.v4i1.51

Abstract

In this paper we consider $L_{\overline{p}, \overline\alpha, \overline{\tau}}^{*}(\mathbb{T}^{m})$ 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.
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