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Mat. Sb. (N.S.), 1982, Volume 119(161), Number 4(12), Pages 564–583 (Mi msb2901)  

This article is cited in 14 scientific papers (total in 14 papers)

On a problem of Hardy-Littlewood

È. A. Storozhenko


Abstract: This work gives an estimate for the quasinorm of the $k$th derivative of a function in the Hardy space $H^p$, $0<p\leqslant\infty$, using a modulus of continuity of order $k$, specially introduced for $H^p$. Also considered are applications of the results to the problem of imbedding of Hardy classes and the theory of approximation.
Bibliography: 26 titles.

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English version:
Mathematics of the USSR-Sbornik, 1984, 47:2, 557–577

Bibliographic databases:

UDC: 517.51
MSC: Primary 41A17, 41A25; Secondary 41A40, 42B30
Received: 01.03.1982

Citation: È. A. Storozhenko, “On a problem of Hardy-Littlewood”, Mat. Sb. (N.S.), 119(161):4(12) (1982), 564–583; Math. USSR-Sb., 47:2 (1984), 557–577

Citation in format AMSBIB
\Bibitem{Sto82}
\by \`E.~A.~Storozhenko
\paper On~a problem of Hardy-Littlewood
\jour Mat. Sb. (N.S.)
\yr 1982
\vol 119(161)
\issue 4(12)
\pages 564--583
\mathnet{http://mi.mathnet.ru/msb2901}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=682500}
\zmath{https://zbmath.org/?q=an:0527.30022}
\transl
\jour Math. USSR-Sb.
\yr 1984
\vol 47
\issue 2
\pages 557--577
\crossref{https://doi.org/10.1070/SM1984v047n02ABEH002659}


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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. A. A. Pekarskii, “Inequalities of Bernstein type for derivatives of rational functions, and inverse theorems of rational approximation”, Math. USSR-Sb., 52:2 (1985), 557–574  mathnet  crossref  mathscinet  zmath
    2. Pekarskii A., “Direct and Inverse-Theorems of Rational Approximation of the Hardy Class”, Dokl. Akad. Nauk Belarusi, 28:2 (1984), 111–114  mathscinet  isi
    3. V. I. Kolyada, “Estimates of rearrangements and imbedding theorems”, Math. USSR-Sb., 64:1 (1989), 1–21  mathnet  crossref  mathscinet  zmath
    4. Storozhenko E., “Smoothness and Derivatives of Functions in Hp(Bn) Spaces”, Vestn. Mosk. Univ. Seriya 1 Mat. Mekhanika, 1988, no. 4, 13–16  mathscinet  isi
    5. Pavlovic M., “On the Moduli of Continuity of Hp Functions with O-Less-Than-P-Less-Than-1”, Proc. Edinb. Math. Soc., 35:Part 1 (1992), 89–100  crossref  mathscinet  zmath  isi
    6. Trigub R., “The Multipliers in Hardy-Spaces H(P)(D(M)) for Rho-Epsilon (0, 1) and Approximation Properties of Summation Methods of Power-Series”, Dokl. Akad. Nauk, 335:6 (1994), 697–699  mathnet  mathscinet  zmath  isi
    7. È. A. Storozhenko, Yu. V. Kryakin, “Whitney's theorem in the $L^p$-metric, $0<p<\infty$”, Sb. Math., 186:3 (1995), 435–445  mathnet  crossref  mathscinet  zmath  isi
    8. Dyakonov K., “Besov Spaces and Outer Functions”, Mich. Math. J., 45:1 (1998), 143–157  crossref  mathscinet  zmath  isi
    9. S. G. Pribegin, “A method of approximation in $H^p$, $0<p\leqslant 1$”, Sb. Math., 192:11 (2001), 1705–1719  mathnet  crossref  crossref  mathscinet  zmath  isi
    10. Yuri Kryakin, Walter Trebels, “q-Moduli of Continuity in Hp(), p>0, and an Inequality of Hardy and Littlewood”, Journal of Approximation Theory, 115:2 (2002), 238  crossref
    11. S. G. Pribegin, “A Method for Summing Fourier Integrals for Functions from $H^p(E_{2n}^+)$, $0<p<\infty$”, Math. Notes, 82:5 (2007), 643–652  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    12. Pavlovic M., “Remarks on l-P-Oscillation of the Modulus of a Holomorphic Function”, J. Math. Anal. Appl., 326:1 (2007), 1–11  crossref  mathscinet  zmath  isi  elib
    13. S. G. Pribegin, “Some summability methods for power series of functions in $H^p(D^n)$, $0<p<\infty$”, Sb. Math., 200:2 (2009), 243–260  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    14. P. Galanopoulos, A.G. Siskakis, G. Stylogiannis, “Mean Lipschitz conditions on Bergman space”, Journal of Mathematical Analysis and Applications, 2014  crossref
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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