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

This article is cited in 2 scientific papers (total in 2 papers)

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
Received: October 23, 2015

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
\Bibitem{BimSma16}
\by A.~U.~Bimendina, E.~S.~Smailov
\paper Fourier--Price coefficients of class GM and best approximations of functions in the Lorentz space $L_{p\theta}[0,1)$, $1<p<+\infty$, $1<\theta<+\infty$
\inbook Function spaces, approximation theory, and related problems of mathematical analysis
\bookinfo Collected papers. In commemoration of the 110th anniversary of Academician Sergei Mikhailovich Nikol'skii
\serial Tr. Mat. Inst. Steklova
\yr 2016
\vol 293
\pages 83--104
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/tm3706}
\crossref{https://doi.org/10.1134/S0371968516020060}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3628472}
\elib{https://elibrary.ru/item.asp?id=26344471}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2016
\vol 293
\pages 77--98
\crossref{https://doi.org/10.1134/S0081543816040064}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000380722200006}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84979995356}


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    Citing articles on Google Scholar: Russian citations, English citations
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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  crossref  isi  scopus
    2. S. S. Volosivets, “Series in Multiplicative Systems in Lorentz Spaces”, Math. Notes, 102:3 (2017), 310–324  mathnet  crossref  crossref  mathscinet  isi  elib
  • Труды Математического института им. В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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