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On the Makarov law of the iterated logarithm
Author(s):
Hå kan
Hedenmalm;
Ilgiz
Kayumov
Journal:
Proc. Amer. Math. Soc.
135
(2007),
2235-2248.
MSC (2000):
Primary 35R35, 35Q35;
Secondary 31A05, 31C12, 53B20, 76D27
Posted:
February 6, 2007
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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.
References:
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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:
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
Posted:
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
Copyright of article:
Copyright
2007,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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