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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
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
Citation:
È. A. Storozhenko, V. G. Krotov, P. Oswald, “Direct and converse theorems of Jackson type in $L^p$ spaces, $0<p<1$”, Mat. Sb. (N.S.), 98(140):3(11) (1975), 395–415; Math. USSR-Sb., 27:3 (1975), 355–374
Linking options:
https://www.mathnet.ru/eng/sm3717https://doi.org/10.1070/SM1975v027n03ABEH002519 https://www.mathnet.ru/eng/sm/v140/i3/p395
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Abstract page: | 1056 | Russian version PDF: | 331 | English version PDF: | 37 | References: | 78 | First page: | 1 |
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