PDF files of articles are only available for institutions which have paid for the online version upon signing an Institutional User License.

Some Banach spaces of Dirichlet series

Volume 226 / 2015

Maxime Bailleul, Pascal Lefèvre Studia Mathematica 226 (2015), 17-55 MSC: Primary 30H10, 30H20. DOI: 10.4064/sm226-1-2

Abstract

The Hardy spaces of Dirichlet series, denoted by $ \mathcal {H}^p$ ($p\geq 1$), 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 $L^p$-generalizations of spaces of Dirichlet series, particularly two families of Bergman spaces, denoted $ \mathcal {A}^p$ and $ \mathcal {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 $H^p({\mathbb D })$ embed into Bergman spaces on the unit disk.

Authors

  • Maxime BailleulUniv Lille-Nord-de-France UArtois
    Laboratoire de Mathématiques de Lens EA 2462
    Fédération CNRS Nord-Pas-de-Calais FR 2956
    F-62 300 Lens, France
    e-mail
  • Pascal LefèvreUniv Lille-Nord-de-France UArtois
    Laboratoire de Mathématiques de Lens EA 2462
    Fédération CNRS Nord-Pas-de-Calais FR 2956
    F-62 300 Lens, France
    e-mail

Search for IMPAN publications

Query phrase too short. Type at least 4 characters.

Rewrite code from the image

Reload image

Reload image