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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A necessary and sufficient condition for Bloch functions
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by Richard M. Timoney PDF
Proc. Amer. Math. Soc. 71 (1978), 263-266 Request permission

Abstract:

A necessary and sufficient condition is given for a subset $E \subseteq {\mathbf {C}}$ to satisfy \[ \begin {array}{*{20}{c}} {\operatorname {Sup}\{ |f’(z)|(1 - |z{|^2})|z \in {f^{ - 1}}(E)\} < \infty } \\ { \Rightarrow \operatorname {Sup}\{ |f’(z)|(1 - |z{|^2})|z \in D\} < \infty } \\ \end {array} \] 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
  • © Copyright 1978 American Mathematical Society
  • 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