Some Banach spaces of Dirichlet series

• Autorzy: Maxime Bailleul , Pascal Lefèvre
• Języki publikacji: EN

Abstrakty

EN

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 $L^{p}$-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.

Kategorie tematyczne

• 30H20: Bergman spaces, Fock spaces
• 30H10: Hardy spaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2015
• Tom: 226
• Numer: 1
• Strony: 17-55

Daty

wydano

2015

Twórcy

autor

Maxime Bailleul

• Univ 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

autor

Pascal Lefèvre

• Univ 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

Identyfikatory

DOI

10.4064/sm226-1-2