ABSOLUTELY SUMMING CARLESON EMBEDDINGS ON BERGMAN SPACES
Résumé
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.
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