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

2024/01/18 by Carando, Daniel, Defant, Andreas, Marceca, Felipe +2
#30B50 #30H10 #43A17 #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2401.09996

Abstract

For a general Dirichlet series ∑ a_n e^{-λ_n s} with frequency λ=(λ_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(λ) that encode the minimum translation necessary for series in the Hardy space H_p(λ) to have absolutely convergent coefficients.

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