A THEOREM OF LOHWATER AND PIRANIAN

被引：4
|
作者：
Danielyan, Arthur A. [1 ]
机构：
[1] Univ S Florida, Dept Math & Stat, Tampa, FL 33620 USA
来源：
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2016年 / 144卷 / 09期
关键词：
Bounded analytic function; Fatou's theorem; radial limit; F-sigma set;
D O I：
10.1090/proc/13083
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
By a well-known theorem of Lohwater and Piranian, for any set E on vertical bar z vertical bar = 1 of type Fs and of measure zero there exists a bounded analytic function in vertical bar z vertical bar < 1 which fails to have radial limits exactly at the points of E. We show that this theorem is an immediate corollary of Fatou's interpolation theorem of 1906.
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页码：3919 / 3920
页数：2
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