Integral means and boundary limits of Dirichlet series

被引：37

作者：

Saksman, Eero ^{[1
]}

Seip, Kristian ^{[2
]}

机构：

[1] Univ Helsinki, Dept Math & Stat, FI-00014 Helsinki, Finland

[2] Norwegian Univ Sci & Technol, Dept Math Sci, NO-7491 Trondheim, Norway

来源：

BULLETIN OF THE LONDON MATHEMATICAL SOCIETY | 2009年 / 41卷

基金：

芬兰科学院;

关键词：

HARDY-SPACES;

D O I：

10.1112/blms/bdp004

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

This paper deals with the boundary behaviour of functions in the Hardy spaces H(p) for ordinary Dirichlet series. The main result, answering a question of Hedenmalm, shows that the classical Carlson theorem on integral means does not extend to the imaginary axis for functions in H(infinity), that is, for the ordinary Dirichlet series in H(infinity) of the right half-plane. We discuss an important embedding problem for H(p), the solution of which is only known when p is an even integer. Viewing H(p) as Hardy spaces of the infinite-dimensional polydisc, we also present analogues of Fatou's theorem.

引用

页码：411 / 422

页数：12