Weighted estimates for Schr\"odinger-Calder\'on-Zygmund operators with exponential decay

TL;DR

This paper establishes weighted boundedness for Schr"odinger-Calderón-Zygmund operators with exponential decay kernels and characterizes the associated weight classes via maximal operators, also analyzing related operators with generalized Schr"odinger operators.

Contribution

It introduces new weighted boundedness results for operators with exponential decay kernels and characterizes weight classes through maximal operators, extending analysis to generalized Schr"odinger operators.

Findings

Weighted boundedness results for exponential decay kernels

Characterization of weight classes via maximal operators

Boundedness of operators related to generalized Schr"odinger operators

Abstract

In this work we obtain weighted boundedness results for singular integral operators with kernels exhibiting exponential decay. We also show that the classes of weights are characterized by a suitable maximal operator. Additionally, we study the boundedness of various operators associated with the generalized Schr\"odinger operator $-\Delta + \mu$, where $\mu$ is a nonnegative Radon measure in $\mathbb{R}^d$, for $d\geq 3$.