Riesz transforms for $1\le p\le 2$

It has been asked (see R. Strichartz, Analysis of the Laplacian$\dotsc$, J. Funct. Anal. 52 (1983), 48–79) whether one could extend to a reasonable class of non-compact Riemannian manifolds the $L^p$ boundedness of the Riesz transforms that holds in $\mathbb {R}^n$. Several partial answers have be... View More