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Article Dans Une Revue Mathematische Annalen Année : 2022

Convergence and almost sure properties in Hardy spaces of Dirichlet series

Résumé

Given a frequency $\lambda$, we study general Dirichlet series $\sum a_n e^{-\lambda_n s}$. First, we give a new condition on $\lambda$ which ensures that a somewhere convergent Dirichlet series defining a bounded holomorphic function in the right half-plane converges uniformly in this half-plane, improving classical results of Bohr and Landau. Then, following recent works of Defant and Schoolmann, we investigate Hardy spaces of these Dirichlet series. We get general results on almost sure convergence which have an harmonic analysis flavour. Nevertheless, we also exhibit examples showing that it seems hard to get general results on these spaces as spaces of holomorphic functions.
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Dates et versions

hal-03103584 , version 1 (08-01-2021)

Identifiants

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Frédéric Bayart. Convergence and almost sure properties in Hardy spaces of Dirichlet series. Mathematische Annalen, 2022, 382, pp.1485-1515. ⟨10.1007/s00208-021-02239-x⟩. ⟨hal-03103584⟩
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