程丽娟副教授，杭州师范大学

In this talk, I will introduce the recent results on $L^p$-boundedness of covariant Riesz transform on differential forms on a class of non-compact weighted Riemannian manifolds for $p\in (1,2]$ without assuming any hypothesis on the derivatives of curvature. As an application, the Calderón-Zygmund inequality for $p\in (1,2]$ on weighted manifolds has been established by only using the curvature-dimension condition. This is a joint work with Anton Thalmaier and Feng-Yu Wang.