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arXiv · 2401.09996

Hypercontractivity and strips of convergence in Hardy spaces of general Dirichlet series

Daniel Carando·Andreas Defant·Felipe Marceca·Ingo Schoolmann·Pablo Sevilla-Peris
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Abstract

For a general Dirichlet series $\sum a_n e^{-\lambda_n s}$ with frequency $\lambda=(\lambda_n)_n$, we study how horizontal translation (i.e. convolution with a Poisson kernel) improves its integrability properties. We characterize hypercontractive frequencies in terms of their additive structure answering some questions posed by Bayart. We also provide sharp bounds for the strips $S_p(\lambda)$ that encode the minimum translation necessary for series in the Hardy space $\mathcal{H}_p(\lambda)$ to have absolutely convergent coefficients.

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Daniel Carando, Andreas Defant, Felipe Marceca, Ingo Schoolmann, Pablo Sevilla-Peris. 2024-01-18. Hypercontractivity and strips of convergence in Hardy spaces of general Dirichlet series. https://arxiv.org/abs/2401.09996

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