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Sibirsk. Mat. Zh., 2003, Volume 44, Number 6, Pages 1273–1279 (Mi smj1254)  

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

A distortion theorem for univalent gap series

I. R. Kayumov

N. G. Chebotarev Research Institute of Mathematics and Mechanics, Kazan State University

Abstract: We prove a distortion theorem for conformal mappings of the unit disk for which $\log f'$ is representable as the Hadamard gap series. This theorem implies in particular that such conformal mapping is “almost” bounded, i.e., for every $\varepsilon>0$, there is a positive constant $C_{\varepsilon}$ such that $|f(z)|\leqslant C_{\varepsilon}(1-|z|)^{-\varepsilon}$.

Keywords: conformal mapping, univalent function, gap series, Loewner equation

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English version:
Siberian Mathematical Journal, 2003, 44:6, 997–1002

Bibliographic databases:

UDC: 517.54
Received: 17.04.2003
Revised: 02.07.2003

Citation: I. R. Kayumov, “A distortion theorem for univalent gap series”, Sibirsk. Mat. Zh., 44:6 (2003), 1273–1279; Siberian Math. J., 44:6 (2003), 997–1002

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, “Spectrum of integral means and the modified Bessel function of zero order”, St. Petersburg Math. J., 17:3 (2006), 453–463  mathnet  crossref  mathscinet  zmath
    2. I. R. Kayumov, D. V. Maklakov, F. D. Kayumov, “Estimates of a spectrum of the integral means for lacunary series”, Russian Math. (Iz. VUZ), 58:10 (2014), 67–72  mathnet  crossref
    3. 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
  • Сибирский математический журнал Siberian Mathematical Journal
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