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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Existence of angular derivative for a class of strip domains


Author: Swati Sastry
Journal: Proc. Amer. Math. Soc. 123 (1995), 1075-1082
MSC: Primary 30C35
MathSciNet review: 1242103
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Abstract: A strip domain R is said to have an angular derivative if for each conformal map $ \phi :R \to S = \{ z:\vert\operatorname{Im} z\vert < 1/2\} $ the limit $ \lim (\phi (w) - w)$ exists and is finite as $ \operatorname{Re} w \to + \infty $. Rodin and Warschawski considerd a class of strip domains for which the euclidean area of $ S\backslash R'$ is finite, where $ R'$ denotes a Lipschitz approximation of $ R, R' \subset R$. They showed that a sufficient condition for an angular derivative to exist is that the euclidean area of $ R'\backslash S$ be finite. We prove that this condition is also necessary.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1995-1242103-6
PII: S 0002-9939(1995)1242103-6
Article copyright: © Copyright 1995 American Mathematical Society