Composition operators on weighted Bergman spaces of Dirichlet series

Maxime Bailleul (1)

1 LML - Laboratoire de Mathématiques de Lens

We study boundedness and compactness of composition operators on weighted Bergman spaces of Dirichlet series. Particularly, we obtain in some speci c cases, upper and lower bounds of the essential norm of these operators and a criterion of compactness on classicals weighted Bergman spaces. Moreover, a su cient condition of compactness is obtained using the notion of Carleson's measure.

Mots clés: Weighted Bergman spaces; Carleson measure; Composition operator; Dirichlet series; essential norm; generalized Nevanlinna counting function

Domaines: Analyse fonctionnelle [math.FA]

Maxime Bailleul. Composition operators on weighted Bergman spaces of Dirichlet series. 2014. ⟨hal-00938088⟩