H_p-theory of general Dirichlet series

2018/11/22 by Andreas Defant, Defant, Andreas, Ingo Schoolmann +1
Mathematics · #Advanced Banach Space Theory #Advanced Harmonic Analysis Research #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.1811.09182

openalex publication_date 2018/11/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Inspired by results of Bayart on ordinary Dirichlet series ∑ a_n n^-s, the main purpose of this article is to start an H_p-theory of general Dirichlet series ∑ a_n e^-λ_ns. Whereas the H_p-theory of ordinary Dirichlet series, in view of an ingenious identification of Bohr, can be seen as a sub-theory of Fourier analysis on the infinite dimensional torus \mathbbT^∞, the H_p-theory of general Dirichlet series is build as a sub-theory of Fourier analysis on certain compact abelian groups, including the Bohr compactification ℝ of the reals. Our approach allows to extend various important facts on Hardy spaces of ordinary Dirichlet series to the much wider setting of H_p-spaces of general Dirichlet series.

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