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

Author(s): Ilgiz Kayumov
Journal: Proc. Amer. Math. Soc. 130 (2002), 1005-1007.
MSC (2000): Primary 30C55, 30C50
Posted: November 28, 2001
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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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Ch. Pommerenke, Boundary Behaviour of Conformal Maps, Springer-Verlag, Berlin, 1992. MR 95b:30008

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S. Rohde, Hausdorffmas und Randverhalten analytischer Functionen, Thesis, Technische Universität, Berlin, 1989.

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L. Carleson, P.W. Jones, On coefficient problems for univalent functions and conformal dimension, Duke Math. J. 66, N 2 (1992), 169-206. MR 93c:30022

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Ph. Kraetzer, Experimental bounds for the universal integral means spectrum of conformal maps, Complex Variables 31 (1996), 305-309. MR 97m:30018

[Kay01]
I.R. Kayumov, Lower estimates for the integral means spectrum, Complex Variables 44 (2001), 165-171.

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Additional Information:

Ilgiz Kayumov
Affiliation: Chebotarev Research Institute, Kazan State University, Universiteskaya 17, 420008 Kazan, Russian Federation
Email: ikayumov@ksu.ru

DOI: 10.1090/S0002-9939-01-06401-2
PII: S 0002-9939(01)06401-2
Keywords: Univalent functions, integral means
Received by editor(s): September 13, 2000
Posted: 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
Copyright of article: Copyright 2001, American Mathematical Society

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