Hua system on irreducible Hermitian symmetric spaces of nontube type.
The paper is a proved affirmation that a real-valued function \(F\) on a non-tube irreductible Hermetian symmetric space is a solution of the Hua system \(H= 0\) if and only if \(F\) is pluriharmonic which generalizes the result [\textit{A. Bonami, D. Buraczewski, E. Damek, A. Hulanicki} and \textit{R. Penney}, J. Funct. Anal. 188, No. 1, 38--74 (2002; Zbl 0999.31005)]. After transfering the problem to Siegel domains, the system may be related by strongly diagonal operators: if \(F\) is annihilated by the Laplace-Beltrami operator and the strongly diagonal Hua operators then \(F\) is pluriharmonic. See also \textit{E. Damek, A. Hulanicki, D. Müller} and \textit{M. M. Peloso} [Geom. Funct. Anal. 10, No. 5, 1090--1117 (2000; Zbl 0969.31007)].
scientific article; zbMATH DE number 2123560
scientific article