Riesz transforms on a class of non-doubling manifolds II

We consider L^p boundedness of the Riesz transform on a class of non-doubling manifolds obtained by taking the connected sum of two Riemannian manifolds which are both a product of a Euclidean space and a closed manifold. We assume that one of the ends has Euclidean dimension equal to 2 which is a special case in which the L^p boundedness of the Riesz transform requires a delicate analysis.