Work

Volterra operator acting on Bergman spaces of Dirichlet series

Year: 2025

Type: article

Abstract: Since their introduction in 1997, Hardy spaces of Dirichlet series have been broadly studied. The increasing interest which they sparked motivated the introduction of new such spaces, as the Bergman spaces A μ p considered here, with μ a probability measure. Similarly, recent lines of research have focused on the study of some classical operators acting on these spaces, like the Volterra operator V g . In this work, we introduce a new family of spaces of Dirichlet series, the Bloch μ -spaces. We can provide, in terms of those spaces, a sufficient condition for this Volterra operator to act boundedly on the spaces A μ p . We also establish a necessary condition for a specific choice of μ . Sufficient and necessary conditions for compactness are also proven. The non-membership in Schatten classes is established, as well as a radicality result for some Bloch space.

Source: Journal of Functional Analysis

DOI: 10.1016/j.jfa.2025.110906

Authors: Carlos Gómez-Cabello, Pascal Lefèvre, Hervé Queffélec

Institutions: Universidad de Sevilla, Université d'Artois, Centre National de la Recherche Scientifique, Laboratoire Paul Painlevé, Université Lille Nord de France

Language: English

Topic: Holomorphic and Operator Theory

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,250

Funders: Agence Nationale de la Recherche, Ministerio de Ciencia e Innovación