Vol. 8, No. 5, 2015

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Sharp $L^p$ bounds for the wave equation on groups of Heisenberg type

Detlef Müller and Andreas Seeger

Vol. 8 (2015), No. 5, 1051–1100
Abstract

Consider the wave equation associated with the sub-Laplacian on groups of Heisenberg type. We construct parametrices using oscillatory integral representations and use them to prove sharp Lp and Hardy space regularity results.

Keywords
wave equation, subelliptic Laplacian, Heisenberg group
Mathematical Subject Classification 2010
Primary: 35L05, 35S30, 42B15, 43A80
Milestones
Received: 13 August 2014
Revised: 17 December 2014
Accepted: 9 February 2015
Published: 28 July 2015
Authors
Detlef Müller
Mathematisches Seminar
Christian-Albrechts-Universität zu Kiel
Ludewig-Meyn-Str. 4
D-24098 Kiel
Germany
Andreas Seeger
Department of Mathematics
University of Wisconsin
Van Vleck Hall, 480 Lincoln Drive
Madison, WI 53706
United States