Covariant Riesz transform on differential forms for 1<p≤2
by Li-Juan Cheng, Anton Thalmaier and Feng-Yu Wang

In this paper, we study Lp-boundedness ( 1<p≤2) of the covariant Riesz transform on differential forms for a class of non-compact weighted Riemannian manifolds without assuming conditions on derivatives of curvature. We present in particular a local version of Lp-boundedness of Riesz transforms under two natural conditions, namely the curvature-dimension condition, and a lower bound on the Weitzenböck curvature endomorphism. As an application, the Calderón-Zygmund inequality for 1<p≤2 on weighted manifolds is derived under the curvature-dimension condition as hypothesis.

The paper is available here:

Li-Juan Cheng
Anton Thalmaier
Feng-Yu Wang

Back to Homepage