Weighted norm inequalities for Schr\"odinger type operators

TL;DR

This paper establishes weighted norm inequalities for Schr"odinger type operators, including Riesz transforms and fractional integrals, extending known results in the context of operators with potentials in the reverse H"older class.

Contribution

It provides new weighted norm inequalities for Schr"odinger operators and their commutators, broadening the scope of existing harmonic analysis results.

Findings

Weighted norm inequalities for Riesz transforms and fractional integrals.

Extension of classical results to Schr"odinger operators with reverse H"older potentials.

Generalization of well-known inequalities in harmonic analysis.

Abstract

Let $L=-\Delta+V$ be a Schr\"{o}dinger operator, where $\Delta $ is the Laplacian operator on $\rz$, while nonnegative potential $V$ belongs to the reverse H\"{o}lder class. In this paper, we establish the weighted norm inequalities for some Schr\"odinger type operators, which include Riesz transforms and fractional integrals and their commutators. These results generalize substantially some well-known results.