ALESSIO MARTINI - UNIVERSITà DI BIRMINGHAM - A FOURIER INTEGRAL OPERATOR APPROACH TO THE SUB-RIEMANNIAN WAVE EQUATION

Let L be a sub-Laplacian on a sub-Riemannian manifold of dimension n. In joint work with Detlef Muller and Sebastiano Nicolussi Golo, we have recently shown that the ranges of validity of spectral multiplier estimates of Mihlin-Hormander type and wave propagator estimates of Miyachi-Peral type for L cannot be wider than the corresponding ranges for the Laplace operator on R^n - despite the lack of ellipticity of L. The proof hinges on a Fourier integral representation for the wave propagator associated with L and nondegeneracy properties of the sub-Riemannian geodesic flow.