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

TL;DR

This paper establishes Carleson embeddings for Bergman spaces on tube domains over symmetric cones and applies these results to characterize bounded operators, providing Schatten class criteria for Toeplitz and Cesàro-type operators.

Contribution

It introduces new Carleson embedding theorems for Bergman spaces on symmetric cone domains and characterizes boundedness and Schatten class membership of related operators.

Findings

Carleson embeddings are established for Bergman spaces on symmetric cone domains.

Bounded Cesàro-type operators are characterized via symbol conditions.

Schatten class criteria are derived for Toeplitz and Cesàro-type operators.

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.