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 Tr. Mat. Inst. Steklova, 2016, Volume 293, Pages 83–104 (Mi tm3706)

Fourier–Price coefficients of class GM and best approximations of functions in the Lorentz space $L_{p\theta}[0,1)$, $1<p<+\infty$, $1<\theta<+\infty$

A. U. Bimendinaa, E. S. Smailovb

a E. A. Buketov Karaganda State University, ul. Universitetskaya 28, Karaganda, 100028 Republic of Kazakhstan
b Institute of Applied Mathematics, Committee on Science, Ministry of Education and Science of the Republic of Kazakhstan, ul. Universitetskaya 28A, Karaganda, 100028 Republic of Kazakhstan

Abstract: 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.

DOI: https://doi.org/10.1134/S0371968516020060

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English version:
Proceedings of the Steklov Institute of Mathematics, 2016, 293, 77–98

Bibliographic databases:

UDC: 517.5

Citation: A. U. Bimendina, E. S. Smailov, “Fourier–Price coefficients of class GM and best approximations of functions in the Lorentz space $L_{p\theta}[0,1)$, $1<p<+\infty$, $1<\theta<+\infty$”, Function spaces, approximation theory, and related problems of mathematical analysis, Collected papers. In commemoration of the 110th anniversary of Academician Sergei Mikhailovich Nikol'skii, Tr. Mat. Inst. Steklova, 293, MAIK Nauka/Interperiodica, Moscow, 2016, 83–104; Proc. Steklov Inst. Math., 293 (2016), 77–98

Citation in format AMSBIB
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• http://mi.mathnet.ru/eng/tm3706
• https://doi.org/10.1134/S0371968516020060
• http://mi.mathnet.ru/eng/tm/v293/p83

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This publication is cited in the following articles:
1. Smailov Y.S., “The Hardy-Littlewood Type Theorems in Besov Spaces With the Haar Basis”, International Conference on Analysis and Applied Mathematics (Icaam 2016), AIP Conference Proceedings, 1759, eds. Ashyralyev A., Lukashov A., Amer Inst Physics, 2016, UNSP 020120
2. S. S. Volosivets, “Series in Multiplicative Systems in Lorentz Spaces”, Math. Notes, 102:3 (2017), 310–324
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