Off-diagonal estimates of some Bergman-type operators on tube domains over symmetric cones

TL;DR

This paper establishes necessary and sufficient conditions for the boundedness of certain positive operators on symmetric cones and applies these results to off-diagonal boundedness of Bergman-type operators in tube domains over these cones.

Contribution

It provides new criteria for operator boundedness on symmetric cones and extends these to off-diagonal estimates for Bergman-type operators in tube domains.

Findings

Derived necessary and sufficient conditions for operator boundedness.

Established off-diagonal boundedness of Bergman-type operators.

Extended results to tube domains over symmetric cones.

Abstract

We obtain some necessary and sufficient conditions for the boundedness of a family of positive operators defined on symmetric cones, we then deduce off-diagonal boundedness of associated Bergman-type operators in tube domains over symmetric cones.