Asymptotic expansions and Hua-harmonic functions on bounded homogeneous domains

Let D be a homogeneous Siegel domain of type II. We prove that every bounded Hua-harmonic function F on D is pluriharmonic. The proof is based on asymptotic expansion of F. The author was partly supported by KBN grant 1 P03A 018 26, Foundation for Polish Sciences, Subsidy 3/99, and by the European Commission via the TMR Network ``Harmonic Analysis', contract no. ERB FMRX-CT97-0159.