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

TL;DR

This paper establishes weighted mixed inequalities for Schr"odinger Calderón-Zygmund operators and their maximal counterparts, providing new insights into Schr"odinger type singular integrals and their inequalities.

Contribution

It introduces the first mixed inequalities for operators related to Schr"odinger operators with critical radius functions, expanding the theoretical framework.

Findings

Weighted mixed inequalities for Schr"odinger Calderón-Zygmund operators

Estimates for associated maximal operators

Applications to Schr"odinger type singular integrals

Abstract

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.