Schatten class Bergman-type and Szego-type operators on bounded symmetric domains

In this paper, we investigate singular integral operators induced by the Bergman kernel and Szego kernel on the irreducible bounded symmetric domain in its standard HarishChandra realization. We completely characterize when Bergman-type operators and Szego-type operators belong to Schatten class operator ideals by several analytic numerical invariants of the bounded symmetric domain. These results not only generalize a recent result on the Hilbert unit ball due to the author and his coauthor but also cover all irreducible bounded symmetric domains. Moreover, we obtain two trace formulae and a new integral estimate related to the Forelli-Rudin estimate. The key ingredient of the proofs involves the function theory on the bounded symmetric domain and the spectrum estimate of Bergman-type and Szego-type operators.(c) 2022 Elsevier Inc. All rights reserved.

Automated summary

In this paper, singular integral operators induced by the Bergman kernel and Szego kernel are investigated on irreducible bounded symmetric domains. The authors completely characterize when these operators belong to Schatten class operator ideals using analytic numerical invariants of the domains. Additionally, two trace formulae and a new integral estimate related to the Forelli-Rudin estimate are obtained.