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Proceedings of the American Mathematical Society

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



Tangential asymptotic values of bounded analytic functions

Authors: U. V. Satyanarayana and Max L. Weiss
Journal: Proc. Amer. Math. Soc. 41 (1973), 167-172
MSC: Primary 30A78
MathSciNet review: 0318498
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Abstract: Suppose $ f$ is a bounded analytic function on the unit disc whose Fatou boundary function is approximately continuous from above at 1 with value 0. It is well known that $ f$ tends to zero radially and therefore along every nontangential arc. Tanaka [3] and Boehme and Weiss [1] have shown that $ f$ must also tend to zero along certain arcs which are tangential from above. The purpose of this paper is to improve their results by producing a larger collection of such tangential arcs along which $ f$ tends to zero. We construct a class of examples to show that our result is actually better.

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Keywords: Bounded analytic function, tangential asymptotic values, approximate continuity
Article copyright: © Copyright 1973 American Mathematical Society