Strichartz Inequalities for the Wave Equation with the Full Laplacian on H-Type Groups

Abstract

We generalize the dispersive estimates and Strichartz inequalities for the solution of the wave equation related to the full Laplacian on H-type groups, by means of Besov spaces defined by a Littlewood-Paley decomposition related to the spectral of the full Laplacian. The dimension of the center on those groups is p and we assume that $p>1$. A key point consists in estimating the decay in time of the $L^{\infty }$ norm of the free solution. This requires a careful analysis due also to the nonhomogeneous nature of the full Laplacian.