Maximum boundary regularity of bounded Hua-harmonic functions on tube   domains
  In this paper we prove that bounded Hua-harmonic functions on tube domains that satisfy some boundary regularity condition are necessarily pluriharmonic. In doing so, we show that a similar theorem is true on one-dimensional extensions of the Heisenberg group or equivalently on the Siegel upper half-plane. 
Aline Bonami, Dariusz Buraczewski, Ewa Damek, Andrzej Hulanicki,   Philippe Jaming