Weighted estimates for commutators of some singular integrals related to Schr\"odinger operators

TL;DR

This paper investigates the boundedness of commutators of singular integrals related to Schrödinger operators on weighted spaces, introducing new BMO functions and weight classes to extend existing results.

Contribution

It establishes boundedness results for commutators of Riesz transforms and fractional integrals associated with Schrödinger operators using new BMO functions and weight classes.

Findings

Boundedness of commutators on weighted spaces.

Extension to new classes of weights.

Application to Schrödinger operator related integrals.

Abstract

Let $L=-\Delta +V$ with non-negative potential $V$ satisfying some appropriate reverse H\"older inequality. In this paper, we study the boundedness of the commutators of some singular integrals associated to $L$ such as Riesz transforms and fractional integrals with the new BMO functions introduced in \cite{BHS1} on the weighted spaces $L^p(w)$ where $w$ belongs to the new classes of weights introduced by \cite{BHS2}.