Weighted and maximally hypoelliptic estimates for the Fokker-Planck Operator with electromagnetic fields

TL;DR

This paper derives sharp weighted and subelliptic estimates for a Fokker-Planck operator influenced by electric and electromagnetic fields, using localization and commutator techniques to control derivatives of the fields.

Contribution

It introduces novel sharp weighted and subelliptic estimates for the Fokker-Planck operator with electromagnetic fields, advancing the understanding of hypoelliptic regularity.

Findings

Established sharp weighted estimates for the operator

Derived subelliptic estimates involving field derivatives

Utilized localization and commutator calculations in proofs

Abstract

We consider a Fokker-Planck operator with electric potential and electromagnetic fields. We establish the sharp weighted and subelliptic estimates, involving the control of the derivatives of electric potential and electromagnetic fields. Our proof relies on a localization argument as well as a careful calculation on commutators.