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

In this paper we consider the sublaplacian L on the unit complex sphere S2n+1 subset of Cn+1, equipped with its natural CR structure, and derive Strichartz estimates with fractional loss of derivatives for the solutions of the free Schriidinger equation associated with L. Our results are stated in terms of certain Sobolev-type spaces that measure the regularity of functions on S2n+1 differently 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.