Maximum boundary regularity of bounded Hua-harmonic functions on tube domains

Aline Bonami (1) , Dariusz Buraczewski (2) , Ewa Damek (2) , Andrzej Hulanicki (2) , Philippe Jaming (1)

1 MAPMO - Mathématiques - Analyse, Probabilités, Modélisation - Orléans
2 Instytut Matematyczny

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.

Mots clés: Heisenberg group; pluriharmonic functions; Tube domains; boundary regularity; Hua-harmonic functions

Domaines: Analyse classique [math.CA]; Variables complexes [math.CV]

Aline Bonami, Dariusz Buraczewski, Ewa Damek, Andrzej Hulanicki, Philippe Jaming. Maximum boundary regularity of bounded Hua-harmonic functions on tube domains. Journal of Geometric Analysis, 2004, 14, pp.457-486. ⟨hal-00001110⟩