# 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} }

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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