2024/02/19 by Carlos Gómez-Cabello, Pascal Lefèvre, Gómez-Cabello, Carlos +3
Mathematics · #Algebraic and Geometric Analysis #Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Meromorphic and Entire Functions
paper · pdf · doi:10.48550/arxiv.2402.12524
openalex publication_date 2024/02/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Since their introduction in 1997, the Hardy spaces of Dirichlet series have been broadly and deeply studied. The increasing interest sparked by these Banach spaces of Dirichlet series motivated the introduction of new such spaces, as the Bergman spaces of Dirichlet series Apμ here considered, where μ is a probability measure on (0,∞). Similarly, recent lines of research have focused their attention on the study of some classical operators acting on these spaces, as it is the case of the Volterra operator Tg. In this work, we introduce a new family of Bloch spaces of Dirichlet series, the Blochμ-spaces, and study some of its most essential properties. Using these spaces we are able to provide a sufficient condition for the Volterra operator Tg to act boundedly on the Bergman spaces Apμ. We also establish a necessary condition for a specific choice of the probability measures μ. Sufficient and necessary conditions for compactness are also proven. The membership in Schatten classes is studied as well. Eventually, a radicality result is established for Bloch spaces of Dirichlet series.