Hua System and Pluriharmonicity for Symmetric Irreducible Siegel Domains of Type II

We consider here a generalization of the Hua system that was proved by Johnson and Korányi to characterize Poisson–Szegő 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:...

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Bibliographic Details
Published in:Journal of functional analysis 2002-01, Vol.188 (1), p.38-74
Main Authors: Bonami, Aline, Buraczewski, Dariusz, Damek, Ewa, Hulanicki, Andrzej, Penney, Richard, Trojan, Bartosz
Format: Article
Language:English
Subjects:
Classical Analysis and ODEs
Complex Variables
Mathematics
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Summary:We consider here a generalization of the Hua system that was proved by Johnson and Korányi to characterize Poisson–Szegő 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.
ISSN:0022-1236
1096-0783
DOI:10.1006/jfan.2001.3823