On uniqueness sets for areally mean $p$-valent functions
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- by Enrique Villamor PDF
- Proc. Amer. Math. Soc. 122 (1994), 1143-1151 Request permission
Abstract:
We study the sets of uniqueness of areally mean p-valent functions in the unit disc. Namely, if $f(z)$ is in this class and has the same angular limit in a set E on the boundary of the unit disc, we prove that if p is small compared to the size of E then $f(z)$ is constant. We then construct an areally mean p-valent function which shows that some condition on the size of the set E must be imposed.References
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Additional Information
- © Copyright 1994 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 122 (1994), 1143-1151
- MSC: Primary 30C45
- DOI: https://doi.org/10.1090/S0002-9939-1994-1211592-4
- MathSciNet review: 1211592