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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
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.

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 2007

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