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Izv. Akad. Nauk SSSR Ser. Mat., 1979, Volume 43, Issue 5, Pages 1121–1144 (Mi izv1749)  

This article is cited in 3 scientific papers (total in 3 papers)

$L_p$-convergence of Bieberbach polynomials

I. V. Kulikov


Abstract: The author proves the estimate
$$ \|p_n-\omega\|_{L_p(G)}\leqslant\frac{c_{p,\varepsilon}}{(\ln\ln n)^{\frac18(1-\theta)-\varepsilon}} $$
where $G\subset\mathbf C$; $p_n(z)\equiv p_n$ are Bieberbach polynomials for the pair $(G,0)$; $\omega(0)=0$, $\omega'(0)=1$, $\omega(z)=\omega\colon G\toż;|z|<R\}$ is a conformal mapping, $\varepsilon>0$, $p\in[1,\infty)$, $0<\theta\equiv\theta(G)<q$. The boundary $\partial G$ is more general than Lipschitz.
Bibliography: 15 titles.

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English version:
Mathematics of the USSR-Izvestiya, 1980, 15:2, 349–371

Bibliographic databases:

UDC: 517.5
MSC: Primary 30C10, 30C35; Secondary 30E10
Received: 17.07.1978

Citation: I. V. Kulikov, “$L_p$-convergence of Bieberbach polynomials”, Izv. Akad. Nauk SSSR Ser. Mat., 43:5 (1979), 1121–1144; Math. USSR-Izv., 15:2 (1980), 349–371

Citation in format AMSBIB
\Bibitem{Kul79}
\by I.~V.~Kulikov
\paper $L_p$-convergence of~Bieberbach polynomials
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1979
\vol 43
\issue 5
\pages 1121--1144
\mathnet{http://mi.mathnet.ru/izv1749}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=552553}
\zmath{https://zbmath.org/?q=an:0443.30049|0427.30032}
\adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?1980IzMat..15..349K}
\transl
\jour Math. USSR-Izv.
\yr 1980
\vol 15
\issue 2
\pages 349--371
\crossref{https://doi.org/10.1070/IM1980v015n02ABEH001240}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1980LD11600006}


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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. I. V. Kulikov, “$W_2^1$$L_\infty$-convergence of Bieberbach polynomials in a Lipschitz domain”, Russian Math. Surveys, 36:5 (1981), 161–162  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    2. I. V. Kulikov, “On the extension of generalized derivatives”, Russian Math. Surveys, 39:1 (1984), 167–168  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    3. Dieter Gaier, “On the convergence of the Bieberbach polynomials in regions with corners”, Constr Approx, 4:1 (1988), 289  crossref  mathscinet  zmath  isi
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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