The heat kernel and the Riesz transforms on the quaternionic Heisenberg groups.
type: Item
instance of: scholarly article
title: The heat kernel and the Riesz transforms on the quaternionic Heisenberg groups.
zbMATH Open document ID: 1054.43009
author: Fuliu Zhu
published in: Pacific Journal of Mathematics
publication date: 2004-09-16T00:00:00Z
review text: Let \(\mathbb H\) be the field of quaternions, then \({\mathbb H}^n\times {\mathbb R}^3\) becomes a nilpotent Lie group called the quaternionic Heisenberg group. By exploiting stochastic integral methods of \textit{B. Gaveau} [C. R. Acad. Sci., Paris, Sér. A 281, 327--328 (1975; Zbl 0321.35041)] developed for the Heisenberg group \({\mathbb C}^n\times {\mathbb R}\) the author computes the heat kernel for the quaternionic Heisenberg group. Adapting methods of \textit{T. Coulhon, D. Müller} and \textit{J. Zienkiewicz} [Math. Ann. 305, No. 2, 369--379 (1996; Zbl 0859.22006)] it is shown that the Riesz transforms on \({\mathbb H}^n\times {\mathbb R}^3\) are bounded uniformly in \(n\).
Mathematics Subject Classification ID: 43A80
Mathematics Subject Classification ID: 22E30
Mathematics Subject Classification ID: 58J35
zbMATH DE Number: 2101068
zbMATH Keywords: heat kernel
zbMATH Keywords: quaternionic Heisenberg group
zbMATH Keywords: Riesz transform
zbMATH Keywords: stochastic integral
MaRDI profile type: Publication
full work available at URL: pjm.2003.209.175
OpenAlex ID: W2024133292
DOI: 10.2140/PJM.2003.209.175
description: scientific article; zbMATH DE number 2101068