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 nilpotent and solvable Lie groups, smoothness and regularity of solutions of PDEs

MSC Classifications:

22E25, 35B65 show english descriptions Nilpotent and solvable Lie groups
Smoothness and regularity of solutions 22E25 - Nilpotent and solvable Lie groups
35B65 - Smoothness and regularity of solutions

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