Erratum to 'Riesz transforms on forms and L~p-Hodge decomposition on complete Riemanian manifolds'

摘要

In [2], the author proved the martingale transform representation formulas for the Riesz transforms on forms over complete Riemannian manifolds, and derived the L~p-norm estimates of the Riesz on forms over complete Riemannian manifolds with suitable curvature conditions. Recently, Banuelos and Baudoin [1] pointed out that there is an error in the martingale transform representation formulas (5.3) and (5.4) stated in [2] due to the fact that e~(ατ) M_(τ,k±1) is not adapted with respect to the filtration F_t = σ(X_s, B_s, s ≤ t), and the proof of the L~p-norm estimates of the Riesz transforms given in [2] contained a gap. They proved a new martingale inequality which can be used to correct this gap.