Geodesic
Direct and converse theorems of Jackson type in $L^p$ spaces, $0$
Sbornik. Mathematics, Tome 27 (1975) no. 3, pp. 355-374

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In this paper the connection between properties of functions and best approximations in classical orthogonal systems is studied in the $L^p$-metric, $0$. 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. 
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     author = {\`E. A. Storozhenko and V. G. Krotov and P. Oswald},
     title = {Direct and converse theorems of {Jackson} type in $L^p$ spaces, $0<p<1$},
     journal = {Sbornik. Mathematics},
     pages = {355--374},
     publisher = {mathdoc},
     volume = {27},
     number = {3},
     year = {1975},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1975_27_3_a3/}
}
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È. A. Storozhenko; V. G. Krotov; P. Oswald. Direct and converse theorems of Jackson type in $L^p$ spaces, $0