Fourier-Price coefficients of class GM and best approximations of functions in the Lorentz space L pθ [0,1), 1<p<+a, 1<θ< plus a

被引：2

作者：

Bimendina, A. U. ^{[1
]}

Smailov, E. S. ^{[2
]}

机构：

[1] EA Buketov Karaganda State Univ, Ul Univ Skaya 28, Karaganda 100029, Kazakhstan

[2] Minist Educ & Sci Republ Kazakhstan, Inst Appl Math, Comm Sci, Ul Univ Skaya 28A, Karaganda 100028, Kazakhstan

来源：

PROCEEDINGS OF THE STEKLOV INSTITUTE OF MATHEMATICS | 2016年 / 293卷 / 01期

关键词：

HARDY-LITTLEWOOD THEOREM; MONOTONE COEFFICIENTS; TRIGONOMETRIC SERIES; INTERPOLATION;

D O I：

10.1134/S0081543816040064

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

For polynomials in the Price system, we establish an inequality of different metrics in the Lorentz spaces. Applying this inequality, we prove a Hardy-Littlewood theorem for the Fourier-Price series with GM sequences of coefficients in the two-parameter Lorentz spaces and in the Nikol'skii-Besov spaces with a Price basis. We also study the behavior of the best approximations of functions by Price polynomials in the metric of the Lorentz space.

引用

页码：77 / 98

页数：22

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Fourier-Price coefficients of class GM and best approximations of functions in the Lorentz space L pθ [0,1), 1&lt;p&lt;+a, 1&lt;θ&lt; plus a

Fourier-Price coefficients of class GM and best approximations of functions in the Lorentz space L pθ [0,1), 1<p<+a, 1<θ< plus a