Hong-Quan Li

The Coulhon--Duong conjecture for the Riesz transform on complete Riemannian manifolds

Let $M$ be a complete, non-compact Riemannian manifold. We prove that its Riesz transform is of weak type $(1,1)$, with constant $2$ for real-valued functions. Consequently, it is bounded on $L^p(M)$ for $1<p\leq2$, with constants depending only on $p$, which proves the Coulhon--Duong conjecture. The proof uses an obst...