The Hardy spaces of Dirichlet series, denoted by (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 -generalizations of spaces of Dirichlet series, particularly two families of Bergman spaces, denoted and . 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 embed into Bergman spaces on the unit disk.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm226-1-2,
author = {Maxime Bailleul and Pascal Lef\`evre},
title = {Some Banach spaces of Dirichlet series},
journal = {Studia Mathematica},
volume = {231},
year = {2015},
pages = {17-55},
zbl = {1319.30042},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm226-1-2}
}
Maxime Bailleul; Pascal Lefèvre. Some Banach spaces of Dirichlet series. Studia Mathematica, Tome 231 (2015) pp. 17-55. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm226-1-2/