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Lower estimate for the integral means spectrum for $p=-1$

Author: Ilgiz Kayumov
Journal: Proc. Amer. Math. Soc. 130 (2002), 1005-1007
MSC (2000): Primary 30C55, 30C50
Published electronically: November 28, 2001
MathSciNet review: 1873773
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Abstract: In this paper we show that there exists a function $f$ bounded and univalent in the unit disk, such that $\int \vert f'(re^{i\theta})\vert^{-1}d\theta \ge C(1-r)^{-0.127}$, $0 \leq r <1.$

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Additional Information

Ilgiz Kayumov
Affiliation: Chebotarev Research Institute, Kazan State University, Universiteskaya 17, 420008 Kazan, Russian Federation

Keywords: Univalent functions, integral means
Received by editor(s): September 13, 2000
Published electronically: November 28, 2001
Additional Notes: This work was supported by Russian Fund of Basic Research (proj 99-01-00366, 99-01-00173)
Communicated by: Juha M. Heinonen
Article copyright: © Copyright 2001 American Mathematical Society