1. CJM 2007 (vol 59 pp. 1301)
|Strichartz Inequalities for the Wave Equation with the Full Laplacian on the Heisenberg Group |
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, G\'erard and Xu concerning the solution of the wave equation related to the Kohn Laplacian.
Keywords:nilpotent and solvable Lie groups, smoothness and regularity of solutions of PDEs