Generalized Cartan and Cartan-Hartogs Domains

Abstract

In this paper, we investigate weighted reproducing kernels on Cartan domains (irreducible bounded symmetric domains) and Cartan-Hartogs domains. For a Hilbert space Hβ of holomorphic functions equipped with generalized canonical metrics g(λⱼ), explicit formulas for the weighted reproducing kernels are obtained. These results are further extended to Cartan-Hartogs domains HD^Bq₀(λⱼ).