Kato-Ponce estimates for fractional sublaplacians

TL;DR

This paper proves commutator estimates for fractional powers of the sublaplacian on the Heisenberg group using pointwise and $L^p$ estimates, advancing the understanding of fractional operators in non-commutative harmonic analysis.

Contribution

It introduces a novel proof technique for commutator estimates involving fractional sublaplacians on the Heisenberg group, utilizing square fractional integrals and Littlewood-Paley theory.

Findings

Established new commutator estimates for fractional sublaplacians.

Developed pointwise and $L^p$ bounds using square fractional integrals.

Applied Littlewood-Paley theory to analyze fractional operators.

Abstract

We give a proof of commutator estimates for fractional powers of the sublaplacian on the Heisenberg group. Our approach is based on pointwise and $L^p$ estimates involving square fractional integrals and Littlewood-Paley square functions.