Some estimates of the Bergman kernel of minimal bounded homogeneous domains

Abstract

We describe the Bergman kernel of any bounded homogeneous domain in a minimal realization relating to the Bergman kernels of the Siegel disks. Taking advantage of this expression, we obtain substantial estimates of the Bergman kernel of the homogeneous domain.

arXiv comment12 pages

References in corpus (1)

• Positive Toepltz operators on the Bergman space of a minimal bounded homogeneous domain

Cited by in corpus (5)

• Sharp pointwise and uniform estimates for $\bar{\partial }$
• On the linearity of origin-preserving automorphisms of quasi-circular domains in ${\mathbb{C}}^n$
• Composition operators on the Bergman spaces of a minimal bounded homogeneous domain
• Positive Toepltz operators on the Bergman space of a minimal bounded homogeneous domain
• Essential norm estimates for positive Toeplitz operators on the weighted Bergman space of a minimal bounded homogeneous domain