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Mat. Zametki, 2004, Volume 76, Issue 4, Pages 510–516 (Mi mz127)  

This article is cited in 1 scientific paper (total in 1 paper)

Sharp Estimates for Integral Means for Three Classes of Domains

I. R. Kayumov


Abstract: In this paper, the following sharp estimate is proved:
$$ \int_0^{2\pi}|F'(e^{i\theta})|^p d\theta \le\sqrt\pi2^{1+p}\frac{\Gamma(1/2+p/2)}{\Gamma(1+p/2)}, \qquad p>-1, $$
where $F$ is the conformal mapping of the domain $D^-=\{\zeta\colon |\zeta|>1\}$ onto the exterior of a convex curve, with $F'(\infty)=1$. For $p=1$ this result is due to Pólya and Shiffer. We also obtain several generalizations of this estimate under other geometric assumptions about the structure of the domain $F(D^-)$.

DOI: https://doi.org/10.4213/mzm127

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English version:
Mathematical Notes, 2004, 76:4, 472–477

Bibliographic databases:

UDC: 517.54
Received: 26.12.2002

Citation: I. R. Kayumov, “Sharp Estimates for Integral Means for Three Classes of Domains”, Mat. Zametki, 76:4 (2004), 510–516; Math. Notes, 76:4 (2004), 472–477

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. I. R. Kayumov, “Obzor po otsenkam spektra integralnykh srednikh konformnykh otobrazhenii”, Uchen. zap. Kazan. un-ta. Ser. Fiz.-matem. nauki, 157, no. 2, Izd-vo Kazanskogo un-ta, Kazan, 2015, 104–115  mathnet  elib
  • Математические заметки Mathematical Notes
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