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.

arXiv commentAll comments are welcome!

References in corpus (5)

• Metric measure spaces with Riemannian Ricci curvature bounded from below
• Bakry-Émery curvature-dimension condition and Riemannian Ricci curvature bounds
• Riemannian Ricci curvature lower bounds in metric measure spaces with $\sigma$-finite measure
• Littlewood--Paley--Stein Estimates for Non-local Dirichlet Forms
• Weighted Littlewood--Paley inequalities for heat flows in $\RCD$ spaces

Cited by in corpus (1)

• Dimension-Free Square Function Estimates for Dunkl Operators