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Zbl 1112.30012
Kim, Yong Chan; Sugawa, Toshiyuki
Norm estimates of the pre-Schwarzian derivatives for certain classes of univalent functions.
(English)
[J] Proc. Edinb. Math. Soc., II. Ser. 49, No. 1, 131-143 (2006). ISSN 0013-0915; ISSN 1464-3839/e

Let $f(z) = z + a_{2} \; z^2 + \cdots$ be analytic in the unit disk $\Bbb{D}$. The authors give sharp estimates for the Becker expression $$\sup\limits_{z\in\Bbb{D}} \; (1 - \vert z\vert ^2) \left\vert \frac{f''(z)}{f'(z)} \right\vert$$ for close-to-convex functions of specified type. In order to show the sharpness, they introduce a kind of maximal operator which may be of independent interest. They also discuss a relation between the subclasses of close-to-convex functions considered and the Hardy spaces.
[Wolfram Koepf (Kassel)]
MSC 2000:
*30C45 Special classes of univalent and multivalent functions

Keywords: Becker expression; univalent function; close-to-convex function

Cited in: Zbl 1135.30018

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