Abstract:
In this paper the connection between properties of functions and best approximations in classical orthogonal systems is studied in the Lp-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 φ(L).
Bibliography: 23 titles.
Citation:
È. A. Storozhenko, V. G. Krotov, P. Oswald, “Direct and converse theorems of Jackson type in Lp spaces, 0<p<1”, Math. USSR-Sb., 27:3 (1975), 355–374
\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/sm3717
https://doi.org/10.1070/SM1975v027n03ABEH002519
https://www.mathnet.ru/eng/sm/v140/i3/p395
This publication is cited in the following 67 articles:
M. R. Langarshoev, S. S. Khorazmshoev, “On the best approximation of some classes of periodic functions in the space L2”, Russian Universities Reports. Mathematics, 30:149 (2025), 56–65
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