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Proceedings of the American Mathematical Society

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

 
 

 

Boundary behavior of univalent functions satisfying a Hölder condition


Author: Matts Essén
Journal: Proc. Amer. Math. Soc. 83 (1981), 83-84
MSC: Primary 30C45
DOI: https://doi.org/10.1090/S0002-9939-1981-0619987-5
MathSciNet review: 619987
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Abstract: Let $ f$ be univalent in the unit disk $ U$ and continuous in $ U \cup T$, where $ T = \partial U$. We prove that if $ f$ satisfies a Hölder condition, then each point in $ f(T)$ is the image of at most finitely many points on $ T$. The bound for the number of preimages depends in a sharp way on the Hölder exponent.


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DOI: https://doi.org/10.1090/S0002-9939-1981-0619987-5
Article copyright: © Copyright 1981 American Mathematical Society

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