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,δ) type, for 1 < s≤ ∞ and 0 < δ ≤ 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.