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

TL;DR

This paper derives precise estimates for how well functions of multiple variables from a Nikol'skii-Besov class can be approximated by trigonometric polynomials within anisotropic Lorentz-Karamata spaces, highlighting the approximation order.

Contribution

It provides order-sharp approximation estimates in anisotropic Lorentz-Karamata spaces for functions from Nikol'skii-Besov classes, a novel result in this context.

Findings

Established order-sharp approximation estimates

Focused on functions in anisotropic Lorentz-Karamata spaces

Used hyperbolic cross trigonometric polynomial approximation

Abstract

In this paper we consider anisotropic Lorentz-Karamata space $2\pi$ of periodic functions of $m$ variables and Nikol'skii--Besov's class . 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-Karamata space.