Bergman-Harmonic Functions on Classical Domains

Abstract

Abstract We study Bergman-harmonic functions on classical domains from a new point of view in this paper. We first establish a boundary pluriharmonicity result for Bergman-harmonic functions on classical domains: a Bergman-harmonic function $u$ on a classical domain $D$ must be pluriharmonic on germs of complex manifolds in the boundary of $D$ if $u$ has some appropriate boundary regularity. Next we give a new characterization of pluriharmonicity on classical domains which may shed a new light on future study of Bergman-harmonic functions. We also prove characterization results for Bergman-harmonic functions on type I domains.