Absolutely summing Carleson embeddings on Bergman spaces.

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. [ABSTRACT FROM AUTHOR]