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Proceedings of the American Mathematical Society

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

 

 

A necessary and sufficient condition for Bloch functions


Author: Richard M. Timoney
Journal: Proc. Amer. Math. Soc. 71 (1978), 263-266
MSC: Primary 30A74
DOI: https://doi.org/10.1090/S0002-9939-1978-0481012-7
MathSciNet review: 0481012
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Abstract: A necessary and sufficient condition is given for a subset $ E \subseteq {\mathbf{C}}$ to satisfy

\begin{displaymath}\begin{array}{*{20}{c}} {\operatorname{Sup}\{ \vert f'(z)\ver... ...1 - \vert z{\vert^2})\vert z \in D\} < \infty } \\ \end{array} \end{displaymath}

when $ f:D \to {\mathbf{C}}$ is analytic. The condition is that the complement of E should not contain large discs.

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1978-0481012-7
Keywords: Bloch function, normal function
Article copyright: © Copyright 1978 American Mathematical Society