On a theorem of Littlewood

被引：1

作者：

Karagulyan, G. A. ^{[1
]}

Safaryan, M. H. ^{[2
]}

机构：

[1] Yerevan State Univ, Fac Math & Mech, Alex Manoogian 1, Yerevan 0025, Armenia

[2] Yerevan State Univ, Alek Manoukyan 1, Yerevan 0049, Armenia

来源：

HOKKAIDO MATHEMATICAL JOURNAL | 2017年 / 46卷 / 01期

关键词：

Fatou theorem; Littlewood theorem; Poisson kernel; NO TANGENTIAL LIMITS; POISSON KERNEL; SQUARE-ROOT; HARMONIC-FUNCTIONS; BOUNDED-FUNCTIONS; APPROACH REGIONS; CONVERGENCE; SHARPNESS; SPACE;

D O I：

10.14492/hokmj/1498788097

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In 1927 Littlewood constructed a bounded holomorphic function on the unit disc, having no tangential boundary limits almost everywhere. This theorem was the complement of a positive theorem of Fatou (1906), establishing almost everywhere non-tangential convergence of bounded holomorphic functions. There are several generalizations of Littlewood's theorem whose proofs are based on the specific properties of holomorphic functions. Applying real variable methods, we extend these theorems to general convolution operators.

引用

页码：87 / 106

页数：20

共 50 条

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