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Tangential Asymptotic Values of Bounded Analytic Functions

U. V. Satyanarayana and Max L. Weiss
Proceedings of the American Mathematical Society
Vol. 41, No. 1 (Nov., 1973), pp. 167-172
DOI: 10.2307/2038834
Stable URL: http://www.jstor.org/stable/2038834
Page Count: 6
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Tangential Asymptotic Values of Bounded Analytic Functions
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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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