Existence of angular derivative for a class of strip domains
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- by Swati Sastry PDF
- Proc. Amer. Math. Soc. 123 (1995), 1075-1082 Request permission
Abstract:
A strip domain R is said to have an angular derivative if for each conformal map $\phi :R \to S = \{ z:|\operatorname {Im} z| < 1/2\}$ 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.References
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Additional Information
- © Copyright 1995 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 123 (1995), 1075-1082
- MSC: Primary 30C35
- DOI: https://doi.org/10.1090/S0002-9939-1995-1242103-6
- MathSciNet review: 1242103