Existence of angular derivative for a class of strip domains

Sastry, Swati

doi:10.1090/S0002-9939-1995-1242103-6

Existence of angular derivative for a class of strip domains
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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.

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