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

A. Bonami·D. Buraczewski·E. Damek·A. Hulanicki·R. Penney·B. Trojan
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Abstract

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.

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A. Bonami, D. Buraczewski, E. Damek, A. Hulanicki, R. Penney, B. Trojan. 2000-09-07. Hua system and pluriharmonicity for symmetric irreducible Siegel domains of type II. https://arxiv.org/abs/math/0009068

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