Sharp Lp bounds for the wave equation on groups of Heisenberg type

Müller, Detlef; Seeger, Andreas

doi:10.2140/apde.2015.8.1051

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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

DOI: 10.2140/apde.2015.8.1051

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 $L^{p}$ 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

Vol. 8, No. 5, 2015