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Mathematics of the USSR-Izvestiya, 1980, Volume 15, Issue 2, Pages 349–371
DOI: https://doi.org/10.1070/IM1980v015n02ABEH001240
(Mi im1749)
 

This article is cited in 4 scientific papers (total in 4 papers)

$L_p$-convergence of Bieberbach polynomials

I. V. Kulikov
References:
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 $(G,0)$; $\omega(0)=0$, $\omega'(0)=1$, $\omega(z)=\omega\colon G\to\{z;|z|<R\}$ 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.
Received: 17.07.1978
Russian version:
Izvestiya Akademii Nauk SSSR. Seriya Matematicheskaya, 1979, Volume 43, Issue 5, Pages 1121–1144
Bibliographic databases:
UDC: 517.5
MSC: Primary 30C10, 30C35; Secondary 30E10
Language: English
Original paper language: Russian
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
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\adsnasa{https://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{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1980LD11600006}
Linking options:
  • https://www.mathnet.ru/eng/im1749
  • https://doi.org/10.1070/IM1980v015n02ABEH001240
  • https://www.mathnet.ru/eng/im/v43/i5/p1121
  • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
    Statistics & downloads:
    Abstract page:376
    Russian version PDF:99
    English version PDF:17
    References:72
    First page:1
     
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