Littlewood--Paley--Stein inequalities on $\text{RCD}(K,\infty )$ spaces

Abstract

The $L^p$ boundedness on vertical Littlewood--Paley square functions for heat flows on $\text{RCD}(K,\infty )$ spaces with $K\in \mathbb{R}$ is proved. With regards to the proof, for $1<p\le 2$, 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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