Estimates of the best approximations of the functions of the Nikol'skii-Besov class in the generalized space of Lorentz

被引：0

作者：

Akishev, G. ^{[1
,2
]}

机构：

[1] LN Gumilyov Eurasian Natl Univ, Nur Sultan 100008, Kazakhstan

[2] Ural Fed Univ, Ekaterinburg 620002, Russia

来源：

ADVANCES IN OPERATOR THEORY | 2021年 / 6卷 / 01期

关键词：

Lorentz space; Besov class; Best approximation; Logarithmic smoothness; TRIGONOMETRIC POLYNOMIALS; DIFFERENT METRICS; INTERPOLATION; INEQUALITY; ANALOGS;

D O I：

10.1007/s43036-020-00108-z

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we consider the generalized Lorentz space of periodic functions of several variables and the Nikol'skii-Besov space of functions. The article establishes a sufficient condition for a function to belong from one generalized Lorentz space to another space in terms of the difference of the partial sums of the Fourier series of a given function. Exact in order estimates of the best approximation by trigonometric polynomials of functions of the Nikol'skii-Besov class are obtained.

引用

页数：36

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