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Proceedings of the American Mathematical Society

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

 

 

Conformal mappings of domains satisfying a wedge condition


Author: Frank David Lesley
Journal: Proc. Amer. Math. Soc. 93 (1985), 483-488
MSC: Primary 30C20; Secondary 30C35
MathSciNet review: 774007
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Abstract: A plane Jordan curve $ \Gamma $ satisfies an interior (exterior) wedge condition if for some $ \alpha \in (0,1)$ there is a fixed wedge of opening $ \alpha \pi $ such that for any $ \omega \in \Gamma $ one may place a wedge inside (outside) $ \Gamma $ with vertex at $ \omega $. Let $ f$ be a conformal mapping of the disk $ D$ onto the interior of $ \Gamma $. We establish Hölder continuity of $ f({f^{ - 1}})$ on $ \partial D(\Gamma )$ with best possible exponents in terms of $ \alpha $.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1985-0774007-0
Keywords: Boundary behavior, Hàlder continuity, cone condition
Article copyright: © Copyright 1985 American Mathematical Society