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This article is cited in 3 scientific papers (total in 3 papers)
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 $|\arg f'(z)|$, $z\in\Delta=\{z:|z|<1\}$ 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.
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
Linking options:
https://www.mathnet.ru/eng/mzm1332https://doi.org/10.4213/mzm1332 https://www.mathnet.ru/eng/mzm/v63/i5/p665
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Abstract page: | 434 | Full-text PDF : | 184 | References: | 56 | First page: | 1 |
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