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Izv. Akad. Nauk SSSR Ser. Mat., 1980, Volume 44, Issue 4, Pages 946–962 (Mi izv1864)  

This article is cited in 11 scientific papers (total in 11 papers)

Theorems of Jackson type in $H^p$$0<p<1$

È. A. Storozhenko


Abstract: In this paper an analogue of Jackson's inequality is established for the Hardy spaces $H^p$ $(0<p<1)$: if $f^{(k)}\in H^p$, then
$$ E_n(f)_p=O((n+1)^{-k}\omega_l(\frac1{n+1},\frac{\partial^kf}{\partial\varphi^k})_{p} ),\quadas\quad n\to\infty, $$
$k=0,1,…$; $ l=1,2,…$, and $\partial^kf/\partial\varphi^k=\lim_{r\to1-0}{\partial^kf(re^{i\varphi})}/{\partial\varphi^k}$.
Bibliography: 15 titles.

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English version:
Mathematics of the USSR-Izvestiya, 1981, 17:1, 203–218

Bibliographic databases:

UDC: 517.51
MSC: Primary 41A17, 42A10; Secondary 30D55
Received: 26.09.1979

Citation: È. A. Storozhenko, “Theorems of Jackson type in $H^p$$0<p<1$”, Izv. Akad. Nauk SSSR Ser. Mat., 44:4 (1980), 946–962; Math. USSR-Izv., 17:1 (1981), 203–218

Citation in format AMSBIB
\Bibitem{Sto80}
\by \`E.~A.~Storozhenko
\paper Theorems of Jackson type in~$H^p$,~$0<p<1$
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1980
\vol 44
\issue 4
\pages 946--962
\mathnet{http://mi.mathnet.ru/izv1864}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=587344}
\zmath{https://zbmath.org/?q=an:0465.42001|0455.42002}
\transl
\jour Math. USSR-Izv.
\yr 1981
\vol 17
\issue 1
\pages 203--218
\crossref{https://doi.org/10.1070/IM1981v017n01ABEH001327}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1981MW12300009}


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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. V. G. Krotov, “On differentiability of functions in $L^p$, $0<p<1$”, Math. USSR-Sb., 45:1 (1983), 101–119  mathnet  crossref  mathscinet  zmath
    2. 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
    3. A. A. Pekarskii, “Classes of analytic functions determined by best rational approximations in $H_p$”, Math. USSR-Sb., 55:1 (1986), 1–18  mathnet  crossref  mathscinet  zmath
    4. Leonardo Colzani, “Jackson theorems in Hardy spaces and approximation by Riesz means”, Journal of Approximation Theory, 49:3 (1987), 240  crossref
    5. R. M. Trigub, “Multipliers in the Hardy spaces $H_p(D^m)$ with $p\in (0,1]$ and approximation properties of summability methods for power series”, Sb. Math., 188:4 (1997), 621–638  mathnet  crossref  crossref  mathscinet  zmath  isi
    6. 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
    7. 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
    8. Guangbin Ren, Mingzhi Wang, “Holomorphic Jackson's theorems in polydiscs”, Journal of Approximation Theory, 134:2 (2005), 175  crossref
    9. 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
    10. 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
    11. YingWei Chen, GuangBin Ren, “Jackson’s theorem in Q p spaces”, Sci China Ser A, 53:2 (2010), 367  crossref
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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