Estimates of the order of approximation of functions of several variables in the generalized Lorentz space
Abstract
In this paper, we consider an anisotropic symmetric space $X(\bar\varphi)$ of $2\pi$-periodic functions of $m$ variables, in particular, the generalized Lorentz space $L_{\bar{\psi},\bar{\tau}}^{*}(\mathbb{T}^{m})$ and the Nikol'skii--Besov class $S_{X(\bar{\varphi}),\bar{\theta}}^{\bar r}B$. We prove an embedding theorem for the Nikol'skii--Besov class into the generalized Lorentz space and establish an upper estimate for the best approximations of functions from the class $S_{X(\bar{\varphi}),\bar{\theta}}^{\bar r}B$ by trigonometric polynomials whose harmonic indices belong to the hyperbolic cross.
Fields of Study & Subjects
Mathematical Approximation and Integration
Differential Equations and Boundary Problems
Advanced Harmonic Analysis Research
Publication details
- Journal / source
- SARAJEVO JOURNAL OF MATHEMATICS
- Publisher
- Academy of Sciences and Arts of Bosnia and Herzegovina
- Volume
- 22
- Issue
- 01
- Pages
- 99–118
- Publication date
- 27 July 2026
- Language
- EN