Hua system on irreducible Hermitian symmetric spaces of nontube type.
type: Item
instance of: scholarly article
title: Hua system on irreducible Hermitian symmetric spaces of nontube type.
zbMATH Open document ID: 1065.32017
author: Dariusz Buraczewski
publication date: 2004-12-20T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/116109
review text: 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)].
reviewed by: Maido Rahula
Mathematics Subject Classification ID: 32M15
zbMATH DE Number: 2123560
zbMATH Keywords: pluriharmonic functions
zbMATH Keywords: Hua system
zbMATH Keywords: Hermitian symmetric spaces
zbMATH Keywords: Siegel domains
MaRDI profile type: Publication
OpenAlex ID: W98780756
cites work: Hua system and pluriharmonicity for symmetric irreducible Siegel domains of type II
cites work: Bounded pluriharmonic functions on symmetric irreducible Siegel domains
cites work: Q3671490
cites work: Boundaries for left-invariant sub-elliptic operators on semidirect products of nilpotent and abelian groups.
cites work: Pluriharmonic \(H^2\) functions on symmetric irreducible Siegel domains
cites work: Hua operators on bounded homogeneous domains in \(\mathbb{C}^ n\) and alternative reproducing kernels for holomorphic functions
cites work: Q4321748
cites work: Q3897665
cites work: Q3331943
cites work: Q4301588
cites work: Discrete series for semisimple Lie groups. II: Explicit determination of the characters
cites work: Q4744553
cites work: Remarks on a theorem of Koranyi and Malliavin on the Siegel upper half plane of rank two
cites work: Differential equations and the Bergman-Silov boundary on the Siegel upper half plane
cites work: The Hua operators on bounded symmetric domains of tube type
cites work: Q4942224
cites work: Poisson formula and compound diffusion associated to an overdetermined elliptic system on the Siegel halfplane of rank two
cites work: Lie groups beyond an introduction
cites work: Rational Inner Functions on Bounded Symmetric Domains
cites work: Realization of Hermitian symmetric spaces as generalized half-planes
cites work: Les équations de Hua d'un domaine borné symétrique du type tube. (The equations of Hua for a bounded symmetric domain of tube type)
cites work: Q4171333
cites work: Q3941676
cites work: Harmonic analysis on the Heisenberg group
DOI: 10.5802/AIF.2011
published in: Annales de l’institut Fourier
description: scientific article; zbMATH DE number 2123560