Erratum to: On the weak $$L^p$$ L p Hodge decomposition and Beurling–Ahlfors transforms on complete Riemannian manifolds

Abstract

Based on a new martingale representation formula, we prove some quantitative upper bound estimates of the Lp-norm of some singular integral operators on complete Riemannian manifolds. This leads us to establish the Weak Lp-Hodge decomposition theorem and to prove the Lp-boundedness of the Beurling–Ahlfors transforms on complete non-compact Riemannian manifolds with non-negative Weitzenbock curvature operator.