Strichartz estimates for the Schroedinger equation for the sublaplacian on complex spheres

Abstract. In this paper we consider the sublaplacian L on the unit complex sphere S^(2n+1) C^(n+1), equipped with its natural CR structure, and derive Strichartz estimates with fractional loss of derivatives for the solutions of the free Schrodinger equation associated with L. Our results are stated in terms of certain Sobolev-type spaces, that measure the regularity of functions on S^(2n+1) dierently according to their spectral localization. Stronger conclusions are obtained for particular classes of solutions, corresponding to initial data whose spectrum is contained in a proper cone of N^2.