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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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
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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
PII: S 0002-9939(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.