Some Banach spaces of Dirichlet series

摘要

The Hardy spaces of Dirichlet series, denoted by H-p (p >= 1), have been studied by Hedenmalm et al. (1997) when p = 2 and by Bayart (2002) in the general case. In this paper we study some LP-generalizations of spaces of Dirichlet series, particularly two families of Bergman spaces, denoted A(p) and B-p. Each could appear as a "natural" way to generalize the classical case of the unit disk. We recover classical properties of spaces of analytic functions: boundedness of point evaluation, embeddings between these spaces and "Littlewood-Paley" formulas when p = 2. Surprisingly; it appears that the two spaces have a different behavior relative to the Hardy spaces and that these behaviors are different from the usual way the Hardy spaces H-p(D) embed into Bergman spaces on the unit disk.