Erratum to: Martingale transforms and $$L^p$$ L p -norm estimates of Riesz transforms on complete Riemannian manifolds

Abstract

In this Erratum, we correct an error in the representation formulas of the Riesz transforms and a gap in the original proof of the L p -norm estimates of the Riesz transforms obtained in the original paper. We would like to point out that, based on the correct representation formulas of the Riesz transforms stated below, and using a new martingale subordination inequality due to Bañuelos and Osekowski (Theorem 2.2 in [2]), we can correct the gap in the original paper without major change in the line of our original argument and to arrive at the original estimates obtained in the original paper.As The online version of the original article can be found under