On the radial limits of analytic and meromorphic functions

Author:
J. S. Hwang

Journal:
Trans. Amer. Math. Soc. **270** (1982), 341-348

MSC:
Primary 30D40

MathSciNet review:
642346

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Abstract: Early in the fifties, A. J. Lohwater proved that if is analytic in and has the radial limit 0 almost everywhere on , then every complex number is an asymptotic value of provided the -points satisfy the following Blaschke condition: , where , . We may, therefore, ask under the hypothesis on how many complex numbers are there whose -points can satisfy the Blaschke condition. We show that there is at most one such number and this one number phenomenon can actually occur if the number is zero.

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DOI:
http://dx.doi.org/10.1090/S0002-9947-1982-0642346-1

Keywords:
Analytic function,
radial limit,
Blaschke condition,
Lusin-Privaloff's class,
boundary behaviour

Article copyright:
© Copyright 1982
American Mathematical Society