Mixed inequalities for operators associated to critical radius functions with applications to Schr\"odinger type operators

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.