Carleson embeddings and two operators on Bergman spaces of tube domains over symmetric cones

Abstract: We prove Carleson embeddings for Bergman spaces of tube domains over symmetric cones, we apply them to characterize symbols of bounded Ces`aro-type operators from weighted Bergman spaces to weighted Besov spaces. We also obtain Schatten class criteria of Toeplitz operators and Ces`aro-type operators on weighted Hilbert-Bergman spaces.