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

TL;DR

This paper investigates $L^p$ estimates for Riesz transforms associated with magnetic Schrödinger operators on $\mathbb{R}^n$, establishing maximal inequalities under conditions involving reverse Hölder inequalities for magnetic fields and electric potentials.

Contribution

It provides new $L^p$ bounds for Riesz transforms of magnetic Schrödinger operators under specific reverse Hölder conditions, advancing understanding of their harmonic analysis properties.

Findings

Established $L^p$ estimates for Riesz transforms

Proved maximal inequalities related to magnetic Schrödinger operators

Identified conditions involving reverse Hölder inequalities

Abstract

The paper concerns the magnetic Schr\"odinger operator on $R^n$. Under certain conditions, given in terms of the reverse H\"older inequality on the magnetic field and the electric potential, we prove some $L^p$ estimates on the Riesz transforms and we establish some related maximal inequalities.