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Mathematics of the USSR-Sbornik, 1975, Volume 27, Issue 3, Pages 355–374
DOI: https://doi.org/10.1070/SM1975v027n03ABEH002519 (Mi sm3717) 		 
This article is cited in 66 scientific papers (total in 66 papers)

Direct and converse theorems of Jackson type in $L^p$ spaces, $0<p<1$

È. A. Storozhenko, V. G. Krotov, P. Oswald
English version PDF (978 kB) Citations (66) Russian version article
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DOI: https://doi.org/10.1070/SM1975v027n03ABEH002519
Abstract: In this paper the connection between properties of functions and best approximations in classical orthogonal systems is studied in the $L^p$-metric, $0<p<1$. Two-sided inequalities are established between moduli of continuity and best approximations in these systems, which are unimprovable in a well-defined sense. Inequalities between best approximations in various metrics are also presented. A number of results are generalized to the classes $\varphi(L)$.
Bibliography: 23 titles.
Received: 07.04.1975
Bibliographic databases:
UDC: 517.5
MSC: Primary 41A50; Secondary 42A56
Language: English
Original paper language: Russian
Citation: È. A. Storozhenko, V. G. Krotov, P. Oswald, “Direct and converse theorems of Jackson type in $L^p$ spaces, $0<p<1$”, Math. USSR-Sb., 27:3 (1975), 355–374
Citation in format AMSBIB
\Bibitem{StoKroOsw75}
\by \`E.~A.~Storozhenko, V.~G.~Krotov, P.~Oswald
\paper Direct and converse theorems of Jackson type in $L^p$ spaces, $0<p<1$
\jour Math. USSR-Sb.
\yr 1975
\vol 27
\issue 3
\pages 355--374
\mathnet{http://mi.mathnet.ru//eng/sm3717}
\crossref{https://doi.org/10.1070/SM1975v027n03ABEH002519}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=402384}
\zmath{https://zbmath.org/?q=an:0314.41004}
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  • https://www.mathnet.ru/eng/sm/v140/i3/p395
    • This publication is cited in the following 66 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics
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    Abstract page:1108
    Russian version PDF:337
    English version PDF:45
    References:91
    First page:1
     
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