Boundedness of Riesz transforms on $\RCD(K, \infty)$ spaces

Understand

For $1<p<\infty$, we prove the $L^p$-boundedness of the Riesz transform operators on metric measure spaces with Riemannian Ricci curvature bounded from below, without any restriction on their dimension.

• This large class of spaces include e.g.
• that of Hilbert spaces endowed with a log-concave probability measure.
• As a consequence, we extend the range of the validity of the Lusin-type approximation of Sobolev by Lipschitz functions, previously obtained by L.