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Strichartz Inequalities for the Wave Equation with the Full Laplacian on the Heisenberg Group

Published online by Cambridge University Press:  20 November 2018

Giulia Furioli ,
Camillo Melzi  and
Alessandro Veneruso
Giulia Furioli
Affiliation:
Dipartimento di Ingegneria Gestionale e dell'Informazione, Università di Bergamo, Viale Marconi 5, I-24044 Dalmine (BG), Italy email: gfurioli@unibg.it
Camillo Melzi
Affiliation:
Dipartimento di Scienze Chimiche, Fisiche e Matematiche, Università dell'Insubria, Via Valleggio 11, I-22100 Como, Italy email: melzi@uninsubria.it
Alessandro Veneruso
Affiliation:
Dipartimento di Matematica, Università di Genova, Via Dodecaneso 35, I-16146 Genova, Italy email: veneruso@dima.unige.it
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Abstract

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We prove dispersive and Strichartz inequalities for the solution of the wave equation related to the full Laplacian on the Heisenberg group, by means of Besov spaces defined by a Littlewood–Paley decomposition related to the spectral resolution of the full Laplacian. This requires a careful analysis due also to the non-homogeneous nature of the full Laplacian. This result has to be compared to a previous one by Bahouri, Gérard and Xu concerning the solution of the wave equation related to the Kohn Laplacian.

Keywords

22E2535B65nilpotent and solvable Lie groupssmoothness and regularity of solutions of PDEs
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 59 , Issue 6 , 01 December 2007 , pp. 1301 - 1322
Copyright
Copyright © Canadian Mathematical Society 2007

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