Characterization of the Poisson integrals for the non-tube bounded symmetric domains
type: Item
instance of: scholarly article
title: Characterization of the Poisson integrals for the non-tube bounded symmetric domains
zbMATH Open document ID: 1123.43005
author: Abdelhamid Boussejra
author: Khalid Koufany
published in: Journal de Mathématiques Pures et Appliquées. Neuvième Série
publication date: 2007-05-03T00:00:00Z
review text: The main result states that the \(L^p\)-range (\(p>1\)) of the Poisson transform on the Shilov boundary for non-tube bounded symmetric domains \(\Omega\) is a Hardy type space for the solutions of a Hua system, which are eigenfunctions of all invariant differential operators on \(\Omega\). The method of proof follows the one used in [\textit{S.Ben Said, T. Oshima} and \textit{N. Shimeno}, Int. Math. Res. Not. 2003, No.~16, 915--931 (2003; Zbl 1020.43005)], which in turn is similar to the one given in [\textit{M. Stoll}, J.~Reine Angew. Math. 271, 63--76 (1974; Zbl 0298.43017)] in the harmonic case. The crucial point is the reduction to the case \(p=2\).
reviewed by: Cornelia-Livia Bejan
Mathematics Subject Classification ID: 43A85
Mathematics Subject Classification ID: 22E30
Mathematics Subject Classification ID: 32A50
Mathematics Subject Classification ID: 32M15
zbMATH DE Number: 5148781
zbMATH Keywords: bounded symmetric domain
zbMATH Keywords: Shilov boundary
zbMATH Keywords: Hua operator
zbMATH Keywords: Poisson transform
MaRDI profile type: Publication
full work available at URL: j.matpur.2007.01.004
OpenAlex ID: W1609706519
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DOI: 10.1016/J.MATPUR.2007.01.004
description: scientific article; zbMATH DE number 5148781