ABSOLUTELY SUMMING CARLESON EMBEDDINGS ON BERGMAN SPACES

Bo He , Joelle Jreis , Pascal Lefèvre (1) , Zengjian Lou

1 LML - Laboratoire de Mathématiques de Lens

In this paper, we focus on Carleson embeddings from Bergman spaces A p into L p (µ), where µ is a positive measure on the unit disk. We describe when this injection is r-summing on A p. We complete the full characterization of such operators when p > 1, and r ≥ 1. As an immediate application, we get the characterization of absolutely summing weighted composition operators on Bergman spaces. In passing we also prove a new connection between the boundedness of the Berezin transform and the Carleson embedding on Bergman spaces.

Mots clés: r-summing operators; Bergman spaces; Carleson embeddings; Berezin transform; Composition operators

Domaines: Analyse fonctionnelle [math.FA]

Bo He, Joelle Jreis, Pascal Lefèvre, Zengjian Lou. ABSOLUTELY SUMMING CARLESON EMBEDDINGS ON BERGMAN SPACES. 2022. ⟨hal-03697585⟩