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- Publisher
- Wiley
- Copyright
- © London Mathematical Society
- ISSN
- 0024-6093
- eISSN
- 1469-2120
- DOI
- 10.1112/blms/bdp004
- Publisher site
- See Article on Publisher Site
Abstract
This paper deals with the boundary behaviour of functions in the Hardy spaces ℋp 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∞, that is, for the ordinary Dirichlet series in H∞ of the right half‐plane. We discuss an important embedding problem for ℋp, the solution of which is only known when p is an even integer. Viewing ℋp as Hardy spaces of the infinite‐dimensional polydisc, we also present analogues of Fatou's theorem.
Journal
Bulletin of the London Mathematical Society – Wiley
Published: Jun 1, 2009