Riesz transform on manifolds with quadratic curvature decay

Abstract

We investigate the $L^p$-boundedness of the Riesz transform on Riemannian manifolds whose Ricci curvature has quadratic decay. Two criterions for the $L^p$-unboundedness of the Riesz transform are given. We recover known results about manifolds that are Euclidean or conical at infinity.