On the boundary behaviour of the Hardy spaces of Dirichlet series and a frame bound estimate
Year: 2011
Type: article
Abstract: A range of Hardy-like spaces of ordinary Dirichlet series, called the Dirichlet–Hardy spaces ℋ p , p ≧ 1, have been the focus of increasing interest among researchers following a paper of Hedenmalm, Lindqvist and Seip [16]. The Dirichlet series in these spaces converge on a certain half-plane, where one may also define the classical Hardy spaces H p . In this paper, we compare the boundary behaviour of elements in ℋ p and H p . Moreover, Carleson measures for the spaces ℋ p are studied. Our main result shows that for certain cases the following statement holds true. Given an interval on the boundary of the half-plane of definition and a function in the classical Hardy space, it is possible to find a function in the corresponding Dirichlet–Hardy space such that their difference has an analytic continuation across this interval.
Authors: Jan-Fredrik Olsen, Eero Saksman
Language: German
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2963557474