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Proceedings of the American Mathematical Society

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

 
 

 

A curvilinear extension of Iversen-Tsuji’s theorem for simply connected domain


Author: Un Haing Choi
Journal: Proc. Amer. Math. Soc. 64 (1977), 47-51
MSC: Primary 30A72
DOI: https://doi.org/10.1090/S0002-9939-1977-0447576-3
MathSciNet review: 0447576
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Abstract: Let D be a simply connected domain with at least two boundary points in the complex plane, and t a boundary point of D. For a meromorphic function $f(z)$ in D, $\lim \sup |f(z)|{\text {as}}\;z \to t$ is given in terms of accessible boundary points and prime ends. This gives a curvilinear extension of Iversen-Tsuji’s Theorem for a simply connected domain.


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Keywords: Capacity, conformal null set, prime end, accessible boundary point, Perron process, Poisson integral, ambiguous point, <!– MATH $\tfrac {1}{2}$ –> <IMG WIDTH="19" HEIGHT="45" ALIGN="MIDDLE" BORDER="0" SRC="images/img1.gif" ALT="$\tfrac {1}{2}$">-dimensional Hausdorff measure
Article copyright: © Copyright 1977 American Mathematical Society