Some Banach spaces of Dirichlet series

Maxime Bailleul, and Pascal Lefèvre. "Some Banach spaces of Dirichlet series." Studia Mathematica 226.1 (2015): 17-55. <http://eudml.org/doc/286350>.

@article{MaximeBailleul2015,
abstract = {The Hardy spaces of Dirichlet series, denoted by $^\{p\}$ (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 $^\{p\}$ 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 $H^\{p\}()$ embed into Bergman spaces on the unit disk.},
author = {Maxime Bailleul, Pascal Lefèvre},
journal = {Studia Mathematica},
keywords = {Dirichlet series; Bergman spaces; Hardy spaces},
language = {eng},
number = {1},
pages = {17-55},
title = {Some Banach spaces of Dirichlet series},
url = {http://eudml.org/doc/286350},
volume = {226},
year = {2015},
}

TY - JOUR
AU - Maxime Bailleul
AU - Pascal Lefèvre
TI - Some Banach spaces of Dirichlet series
JO - Studia Mathematica
PY - 2015
VL - 226
IS - 1
SP - 17
EP - 55
AB - The Hardy spaces of Dirichlet series, denoted by $^{p}$ (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 $^{p}$ 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 $H^{p}()$ embed into Bergman spaces on the unit disk.
LA - eng
KW - Dirichlet series; Bergman spaces; Hardy spaces
UR - http://eudml.org/doc/286350
ER -