# Integral means and boundary limits of Dirichlet series

@article{Saksman2009IntegralMA,
title={Integral means and boundary limits of Dirichlet series},
author={Eero Saksman and Kristian Seip},
journal={Bulletin of the London Mathematical Society},
year={2009},
volume={41}
}
• Published 4 December 2007
• Mathematics
• Bulletin of the London Mathematical Society
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…
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