On Fatou's theorem

被引：3
|
作者：
Danielyan, Arthur A. [1 ]
机构：
[1] Univ S Florida, Dept Math & Stat, Tampa, FL 33620 USA
来源：
ANALYSIS AND MATHEMATICAL PHYSICS | 2020年 / 10卷 / 03期
关键词：
Bounded analytic function; Fatou's theorem; Radial limit; F-sigma set;
D O I：
10.1007/s13324-020-00368-1
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Let E be a set on the unit circle T of C. We prove that there exists an f is an element of H-infinity which has no radial limits on E but has unrestricted limit at each point of T\E if and only if E is an F-sigma of measure zero. The necessity of the condition that E is an F-sigma is almost obvious and the necessity of the condition that E is of measure zero follows from Fatou's theorem.
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页数：4
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