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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Harmonic measure and domains bounded by quasiconformal circles


Author: Donald K. Blevins
Journal: Proc. Amer. Math. Soc. 41 (1973), 559-564
MSC: Primary 30A60; Secondary 30A78
DOI: https://doi.org/10.1090/S0002-9939-1973-0325960-2
MathSciNet review: 0325960
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Abstract: We index the class of quasiconformal circles by $ k$ between zero and one such that $ k = 0$ corresponds to arbitrary Jordan curves and $ k = 1$ to circles. We establish an estimate depending on $ k$ for harmonic measure in a domain bounded by a quasiconformal circle. Applications of this estimate are made to boundary correspondence under conformal maps, Hardy class of certain functions and a Phragmén-Lindelöf theorem.


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DOI: https://doi.org/10.1090/S0002-9939-1973-0325960-2
Keywords: Quasiconformal circles, harmonic measure
Article copyright: © Copyright 1973 American Mathematical Society