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Littlewood--Paley--Stein inequalities on $\textup{RCD}(K,\infty)$ spaces
Huaiqian Li · 2019-05-04 · via math.PR updates on arXiv.org

The $L^p$ boundedness on vertical Littlewood--Paley square functions for heat flows on $\textup{RCD}(K,\infty)$ spaces with $K\in\mathbb{R}$ is proved. With regards to the proof, for $1<p\leq 2$, Stein's analytical method is applied, while for $2<p<\infty$, the probabilistic approach in the sense of Bañuelos--Bogdan--Luks introduced recently is employed.

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