On the Makarov law of the iterated logarithm

Authors:
Hå kan Hedenmalm and Ilgiz Kayumov

Journal:
Proc. Amer. Math. Soc. **135** (2007), 2235-2248

MSC (2000):
Primary 35R35, 35Q35; Secondary 31A05, 31C12, 53B20, 76D27

Published electronically:
February 6, 2007

MathSciNet review:
2299501

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We obtain considerable improvement of Makarov's estimate of the boundary behavior of a general conformal mapping from the unit disk to a simply connected domain in the complex plane. We apply the result to improve Makarov's comparison of harmonic measure with Hausdorff measure on simply connected domains.

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Additional Information

**Hå kan Hedenmalm**

Affiliation:
Department of Mathematics, The Royal Institute of Technology, S – 100 44 Stockholm, Sweden

Email:
haakanh@math.kth.se

**Ilgiz Kayumov**

Affiliation:
Institute of Mathematics and Mechanics, Kazan State University, 420008 Kazan, Russia

Email:
ikayumov@ksu.ru

DOI:
http://dx.doi.org/10.1090/S0002-9939-07-08772-2

Keywords:
Conformal mapping,
law of the iterated logarithm

Received by editor(s):
October 26, 2005

Received by editor(s) in revised form:
March 29, 2006

Published electronically:
February 6, 2007

Additional Notes:
Research supported by the Göran Gustafsson Foundation and by the Russian Fund of Basic Research (05-01-00523, 03-01-00015).

Communicated by:
Juha M. Heinonen

Article copyright:
© Copyright 2007
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.