A $p=2$ dichotomy for uniform Riesz transform bounds on stratified Lie groups

Sheng-Chen Mao, Yaojun Wang, Ye Zhang

Let $\mathbb{G}$ be a stratified Lie group and $\mathcal{L}$ be its sub-Laplacian. We prove that the full horizontal Riesz transform ${\nabla }_H{\mathcal{L}}^{-1/2}$ is of weak type $…