The Holomorphic Equivalence of Two Equidimensional Hartogs Domains over Bounded Symmetric Domains

Abstract

This paper is concerned with the biholomorphism of two equidimensional Hartogs type domains over irreducible bounded symmetric domains $H_{\Omega}(p)$ (see (1.1)) which is a Hua construction of Cartan–Hartogs domain. We develop a new simple methods to give an sufficient and necessary condition for the two Hua domains to be biholomorphic equivalent by using the function $\mathcal{L}_{\Omega}(z,\omega)$ (see (1.2)). Furthermore as an application, we can also give an equivalent description for the automorphism of Hua domain.