St. Petersburg Mathematical Society

Author(s): I. R. Kayumov
Translated by: S. V. Kislyakov
Original publication: Algebra i Analiz, tom 17 (2005), vypusk 3.
Journal: St. Petersburg Math. J. 17 (2006), 453-463.
MSC (2000): Primary 30C35
Posted: March 9, 2006
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Abstract: A new characteristic $\beta^*_f(t)$ of a conformal mapping

of the disk $\Bbb D$ onto a simply connected domain is introduced and its relationship with the so-called integral means spectrum $\beta_f(t)$ is studied. The Brennan conjecture (saying that $\beta_f(-2)\le 1$ ) is confirmed in the case where the Taylor series of $\log f'(z)$ is Hadamard lacunary with sufficiently large lacunarity exponent.

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I. R. Kayumov
Affiliation: Kazan State University, Kazan, Russia
Email: ikayumov@ksu.ru

DOI: 10.1090/S1061-0022-06-00914-9
PII: S 1061-0022(06)00914-9
Keywords: Conformal mapping, $\ast$-spectrum of integral means, modified Bessel function
Received by editor(s): 15/JUN/2004
Posted: March 9, 2006
Additional Notes: This article was supported in part by RFBR (grants no. 05--01--00523 and 03-01-00015), and by the NIOKR AN RT foundation
Copyright of article: Copyright 2006, American Mathematical Society

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ISSN: 1547-7371(e) ISSN: 1061-0022(p)

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