Hua system and pluriharmonicity for symmetric irreducible Siegel domains   of type II
  We consider the Johnson-Koranyi-Hua system on symmetric Siegel domains of type two. We prove that all functions which are annihilated by the system and satisfy an H^2 integrability condition are pluriharmonic. So the situation is completely different on type two domains than on tube type domains: it was proved by Johnson and Koranyi that on symmetric tube type domains the system characterizes Poisson-Szego integrals. 
A. Bonami, D. Buraczewski, E. Damek, A. Hulanicki, R. Penney and B.   Trojan