Geodesic
Sharpness of certain Campbell and Pommerenke estimates
Matematičeskie zametki, Tome 63 (1998) no. 5, pp. 665-672.

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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. 
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     title = {Sharpness of certain {Campbell} and {Pommerenke} estimates},
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J. Godula; V. V. Starkov. Sharpness of certain Campbell and Pommerenke estimates. Matematičeskie zametki, Tome 63 (1998) no. 5, pp. 665-672. http://geodesic.mathdoc.fr/item/MZM_1998_63_5_a3/

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