On the $L^p$-estimates of Riesz transforms on forms over complete Riemanian manifolds

Abstract

In our previous paper \cite{Li2010}, we proved a martingale transform representation formula for the Riesz transforms on forms over complete Riemannian manifolds, and proved some explicit $L^p$-norm estimates for the Riesz transforms on complete Riemannian manifolds with suitable curvature conditions. In this paper we correct a gap contained in \cite{Li2010} and prove that the main result obtained in \cite{Li2010} on the $L^p$-norm estimates for the Riesz transforms on forms remain valid. Moreover, we prove a time reversal martingale transform representation formula for the Riesz transforms on forms. Finally, we extend our approach and result to the Riesz transforms acting on Euclidean vector bundles over complete Riemannian manifolds with suitable curvature conditions.

arXiv admin note: substantial text overlap with arXiv:1304.1168

References in corpus (1)

• On the $L^p$-estimates for Beurling-Ahlfors and Riesz transforms on Riemannian manifolds