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Mat. Sb. (N.S.), 1975, Volume 97(139), Number 2(6), Pages 230–241 (Mi msb3649)  

This article is cited in 6 scientific papers (total in 6 papers)

Embedding theorems and best approximations

È. A. Storozhenko


Abstract: We establish necessary and sufficient conditions, in terms of best approximations, for a function in $L^p(0,2\pi)$ ($0<p<1$) to belong to $L^q(0,2\pi)$ ($q<p$). The proofs depend on the properties of equimeasurable functions, which were applied by Ul'yanov in the theory of the embedding of certain classes $H_p^\omega$ for $p\geqslant1$ (RZhMat., 1969, 2B109). We also obtain some relationships among moduli of continuity in different metrics, which let us generalize results of Hardy and Littlewood (Math. Z., 28, № 4 (1928), 612–634) to the case $0<p<1$ and prove converses for nonincreasing functions.
Bibliography: 11 titles.

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English version:
Mathematics of the USSR-Sbornik, 1975, 26:2, 213–224

Bibliographic databases:

UDC: 517.5
MSC: Primary 26A16, 26A86; Secondary 41A50, 42A08
Received: 21.10.1974

Citation: È. A. Storozhenko, “Embedding theorems and best approximations”, Mat. Sb. (N.S.), 97(139):2(6) (1975), 230–241; Math. USSR-Sb., 26:2 (1975), 213–224

Citation in format AMSBIB
\Bibitem{Sto75}
\by \`E.~A.~Storozhenko
\paper Embedding theorems and best approximations
\jour Mat. Sb. (N.S.)
\yr 1975
\vol 97(139)
\issue 2(6)
\pages 230--241
\mathnet{http://mi.mathnet.ru/msb3649}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=404965}
\zmath{https://zbmath.org/?q=an:0337.46032}
\transl
\jour Math. USSR-Sb.
\yr 1975
\vol 26
\issue 2
\pages 213--224
\crossref{https://doi.org/10.1070/SM1975v026n02ABEH002477}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. 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  mathnet  crossref  mathscinet  zmath
    2. V. I. Kolyada, “Rearrangements of functions and embedding theorems”, Russian Math. Surveys, 44:5 (1989), 73–117  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    3. G. A. Akishev, “Obobschennaya sistema Khaara i teoremy vlozheniya v simmetrichnye prostranstva”, Fundament. i prikl. matem., 8:2 (2002), 319–334  mathnet  mathscinet  zmath
    4. G. A. Akishev, “On Orders of Approximation of Function Classes in Lorentz spaces with Anisotropic Norm”, Math. Notes, 81:1 (2007), 3–14  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    5. Yu. S. Kolomoitsev, “On approximation of functions by trigonometric polynomials with incomplete spectrum in $L_p$, $0<p<1$”, J. Math. Sci. (N. Y.), 165:4 (2010), 463–472  mathnet  crossref  elib
    6. N. A. Ilyasov, “Pryamaya teorema v raznykh metrikakh teorii priblizhenii periodicheskikh funktsii s monotonnymi koeffitsientami Fure”, Tr. IMM UrO RAN, 23, no. 3, 2017, 144–158  mathnet  crossref  elib
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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