Boundary behavior of univalent functions satisfying a Hölder condition
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- by Matts Essén PDF
- Proc. Amer. Math. Soc. 83 (1981), 83-84 Request permission
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.References
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- Murray H. Protter and Hans F. Weinberger, Maximum principles in differential equations, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1967. MR 0219861
Additional Information
- © Copyright 1981 American Mathematical Society
- 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