Riesz transforms on connected sums

Assume that M 0 is a complete Riemannian manifold with Ricci curvature bounded from below and that M 0 satisfies a Sobolev inequality of dimension ν > 3 . Let M be a complete Riemannian manifold isometric at infinity to M 0 and let p ∈ ( ν / ( ν - 1 ) , ν ) . The boundedness of the Riesz transform of L p ( M 0 ) then implies the boundedness of the Riesz transform of L p ( M )