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

Abstract

We obtain weighted mixed inequalities for operators associated to a critical radius function. We consider Schrödinger Calderón-Zygmund operators of $(s,\delta )$ type, for $1<s\le \infty$ and $0<\delta \le 1$. 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.

26 pages