  We obtain weighted mixed inequalities for operators associated to a critical
radius function. We consider Schr\"odinger Calder\'on-Zygmund operators of
$(s,\delta)$ type, for $1<s\leq \infty$ and $0<\delta \leq 1$. We also give
estimates of the same type for the associated maximal operators. As an
application, we obtain a wide variety of mixed inequalities for Schr\"odinger
type singular integrals.
  As far as we know, these results are a first approach of mixed inequalities
in the Schr\"odinger setting.
