Smoothing and Strichartz estimates for degenerate Schrödinger-type equations

In this paper we focus on the validity of some fundamental estimates for time-degenerate Schrödinger-type operators. On the one hand we derive global homogeneous smoothing estimates for operators of any order by means of suitable comparison principles (that we shall obtain here). On the other hand, we prove weighted Strichartz-type estimates for time-degenerate Schrödinger operators and apply them to the local well-posedness of the semilinear Cauchy problem. Most of our results apply to nondegenerate operators as well, recovering, in these cases, the known standard results.