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A geometric characterization of $ N\sp{+}$ domains

Authors: Patrick Ahern and William Cohn
Journal: Proc. Amer. Math. Soc. 88 (1983), 454-458
MSC: Primary 30D50; Secondary 31A15
MathSciNet review: 699413
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Abstract: A connected open set $ \mathcal{O} \subseteq {\mathbf{C}}$ is called an $ {N^ + }$ domain if every holomorphic function defined in the unit disc and taking values in $ \mathcal{O}$ is necessarily in the Smirnov class $ {N^ + }$. We show that $ \mathcal{O}$ is an $ {N^ + }$ domain if and only if $ \infty $ is a regular point for the solution of the Dirichlet problem for $ \mathcal{O}$. We get a similar characterization when $ {N^ + }$ is replaced by the class of outer functions.

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Article copyright: © Copyright 1983 American Mathematical Society