Multipliers for Hardy spaces of Dirichlet series

2022/05/16 by T. Vidal, Vidal, Tomás Fernandez, Daniel Galicer +3
Mathematics · #Advanced Harmonic Analysis Research #Holomorphic and Operator Theory #Algebraic and Geometric Analysis

paper · pdf · doi:10.48550/arxiv.2205.07961

Abstract

We characterize the space of multipliers from the Hardy space of Dirichlet series \mathcal H_p into \mathcal H_q for every 1 ≤ p,q ≤ ∞. For a fixed Dirichlet series, we also investigate some structural properties of its associated multiplication operator. In particular, we study the norm, the essential norm, and the spectrum for an operator of this kind. We exploit the existing natural identification of spaces of Dirichlet series with spaces of holomorphic functions in infinitely many variables and apply several methods from complex and harmonic analysis to obtain our results. As a byproduct we get analogous statements on such Hardy spaces of holomorphic functions.

Related

• Fourier multipliers for Hardy spaces of Dirichlet series
• Characterization of multipliers on vector-valued Hardy spaces
• A note on Fourier multipliers on the product Hardy spaces
• Some open questions in analysis for Dirichlet series
• Hardy spaces of general Dirichlet series - a survey