Maximal Inequalities and Riesz Transform Estimates on $L^p$ Spaces for Magnetic Schrodinger Operators II

TL;DR

This paper establishes $L^p$ estimates for Riesz transforms and maximal inequalities for magnetic Schrödinger operators on $\mathbb{R}^n$, linking magnetic field control to electric potential conditions.

Contribution

It provides new $L^p$ bounds and maximal inequalities for Riesz transforms associated with magnetic Schrödinger operators, based on magnetic field and electric potential control.

Findings

Proved $L^p$ estimates for Riesz transforms

Established maximal inequalities related to magnetic Schrödinger operators

Identified conditions linking magnetic field control to electric potential

Abstract

The paper concerns the magnetic Schr\"odinger operator on $R^n$. We prove some $L^p$ estimates on the Riesz transforms and we establish some related maximal inequalities. The conditions that we arrive at, are essentially based on the control of the magnetic field by the electric potential.