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Mat. Zametki, 1998, Volume 63, Issue 5, Pages 665–672 (Mi mz1332)  

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

Sharpness of certain Campbell and Pommerenke estimates

J. Godulaa, V. V. Starkovb

a Maria Curie-Sklodowska University
b Petrozavodsk State University

Abstract: The paper is concerned with the sharpness of some well-known estimates in universal linear-invariant families $\mathscr U_\alpha$ of regular functions. It is shown that the estimate of $|\arg f'(z)|$, $z\in\Delta=ż:|z|<1\}$ obtained by Pommerenke in 1964 is sharp; the extremal function is found. A lower estimate for the Schwarzian derivative in $\mathscr U_\alpha$ is obtained. For $f\in\mathscr U_\alpha$, a sharp estimate of order of the function $f_r(z)=f(rz)/r$ with $r\in(0,1)$ is found; this estimate is applied to solve other problems.

DOI: https://doi.org/10.4213/mzm1332

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English version:
Mathematical Notes, 1998, 63:5, 586–592

Bibliographic databases:

UDC: 517.54
Received: 28.10.1996

Citation: J. Godula, V. V. Starkov, “Sharpness of certain Campbell and Pommerenke estimates”, Mat. Zametki, 63:5 (1998), 665–672; Math. Notes, 63:5 (1998), 586–592

Citation in format AMSBIB
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\by J.~Godula, V.~V.~Starkov
\paper Sharpness of certain Campbell and Pommerenke estimates
\jour Mat. Zametki
\yr 1998
\vol 63
\issue 5
\pages 665--672
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\crossref{https://doi.org/10.4213/mzm1332}
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\transl
\jour Math. Notes
\yr 1998
\vol 63
\issue 5
\pages 586--592
\crossref{https://doi.org/10.1007/BF02312838}
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    This publication is cited in the following articles:
    1. Graf S.Yu., “The Schwarzian Derivatives of Harmonic Functions and Univalence Conditions”, Probl. Anal., 6:2 (2017), 42–56  crossref  mathscinet  zmath  isi  scopus  scopus
  • Математические заметки Mathematical Notes
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