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arXiv · 0712.0492

Integral means and boundary limits of Dirichlet series

Eero Saksman·Kristian Seip
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Abstract

We study the boundary behavior of functions in the Hardy spaces HD^p for ordinary Dirichlet series. Our main result, answering a question of H. Hedenmalm, shows that the classical F. Carlson theorem on integral means does not extend to the imaginary axis for functions in HD^\infty, i.e., for ordinary Dirichlet series in H^\infty of the right half-plane. We discuss an important embedding problem for HD^p, the solution of which is only known when p is an even integer. Viewing HD^p as Hardy spaces of the infinite-dimensional polydisc, we also present analogues of Fatou's theorem.

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Eero Saksman, Kristian Seip. 2007-12-04. Integral means and boundary limits of Dirichlet series. https://doi.org/10.1112/blms%2Fbdp004

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