  In this paper we focus on the validity of some fundamental estimates for
time-degenerate Schr\"{o}dinger-type operators. On 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 Scrh\"{o}dinger
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 well-known standard results.
