In this talk, I will considerSchr\"odinger type operators$H=(-\Delta)^\alpha +a|x|^{-2\alpha}$ with a subcrtical coupling constant $a$ , and mainly talk about several global estimates for the resolvent and the solution to the time-dependent Schr\"odinger equation associated with $H$. We first give {\it the uniform resolvent estimates} of Kato-Yajima type for all $0<\alpha<n/2$，which turn out to be equivalent to {\it Kato smoothing estimates} for the Cauchy problem. Using Kato smoothing estimates, we then can obtain {\it Strichartz estimates} for $\alpha>1/2$ and {\it the uniform Sobolev estimates} of Kenig-Ruiz-Sogge type for $\alpha\ge n/(n+1)$. These completely extend the same properties for the Schr\"odinger operator with the inverse-square potential to the higher-order and fractional cases. Among the results, I also introduce some backgrounds and dispersive estimates of Schr\"odinger operator.