Hua system and pluriharmonicity for symmetric irreducible Siegel domains of type II

Aline Bonami (1) , Dariusz Buraczewski (2) , Ewa Damek (2) , Andrzej Hulanicki (2) , Richard Penney (3) , Bartosz Trojan (2)

1 MAPMO - Mathématiques - Analyse, Probabilités, Modélisation - Orléans
2 Department of Mathematics
3 Department of Mathematics

We consider here a generalization of the Hua system that was proved by Johnson and Korányi to characterize Poisson–SzegImage integrals for Siegel domains of tube-type. We show that the situation is completely different when dealing with non-tube-type symmetric irreducible symmetric domains: then all functions that are annihilated by this second-order system and satisfy an H2-type integrability condition are pluriharmonic functions.

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

Aline Bonami, Dariusz Buraczewski, Ewa Damek, Andrzej Hulanicki, Richard Penney, et al.. Hua system and pluriharmonicity for symmetric irreducible Siegel domains of type II. Journal of Functional Analysis, 2002, vol 188 issue 1, pp.38-74. ⟨hal-00087775⟩