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 $L_{\overline{p}, \overline\alpha, \overline{\tau}}^{*}(\mathbb{T}^{m})$ 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.
Fields of Study & Subjects
Mathematical Approximation and Integration
Differential Equations and Boundary Problems
Advanced Harmonic Analysis Research
Publication details
- Journal / source
- Hilbert Journal of Mathematical Analysis.
- Publisher
- Komunitas Analisis Matematika Indonesia
- Volume
- 4
- Issue
- 1
- Pages
- 026–045
- Publication date
- 10 August 2026
- Language
- EN