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

Furioli, Giulia ; Melzi, Camillo ; Veneruso, Alessandro

Canadian journal of mathematics, Tome 59 (2007) no. 6, pp. 1301-1322

Résumé

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.

Détail

DOI : 10.4153/CJM-2007-056-1

Mots-clés : 22E25, 35B65, nilpotent and solvable Lie groups, smoothness and regularity of solutions of PDEs

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