Maximum boundary regularity of bounded Hua-harmonic functions on tube domains

2004/02/03 by Aline Bonami, Dariusz Buraczewski, Ewa Damek +2
Mathematics · #math.CA #math.CV #msc:22E30 #msc:32M15 #msc:35J25 #msc:58J32

paper · pdf

published as Journal of Geometric Analysis 14 (2004) 457-486

arxiv created 2004/02/03 · arxiv updated 2009/12/01

Abstract

In this paper we prove that bounded Hua-harmonic functions on tube domains that satisfy some boundary regularity condition are necessarily pluriharmonic. In doing so, we show that a similar theorem is true on one-dimensional extensions of the Heisenberg group or equivalently on the Siegel upper half-plane.

Related

• Boundary behavior p-harmonic functions in the Heisenberg group
• Bounded pluriharmonic functions and holomorphic functions on Teichmüller space
• HW^2,2_{\rm loc}-regularity for p-harmonic functions in Heisenberg groups
• Boundary regularity for manifold constrained p(x)-harmonic maps
• Hua system and pluriharmonicity for symmetric irreducible Siegel domains of type II