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Mixed inequalities for operators associated to critical radius functions with applications to Schrödinger type operators

We obtain weighted mixed inequalities for operators associated to a critical radius function. We consider Schrödinger Calderón-Zygmund operators of $(s,δ)$ type, for $1<s\leq \infty$ and $0<δ\leq 1$. 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 Schrödinger type singular integrals. As far as we know, these results are a first approach of mixed inequalities in the Schrödinger setting.