Riesz transforms on connected sums

Abstract

Assume that M0 is a complete Riemannian manifold with Ricci curvature bounded from below and that M0 satisfies a Sobolev inequality of dimension ν > 3. Let M be a complete Riemannian manifold isometric at infinity to M0 and let p ε (ν/(ν - 1), ν). The boundedness of the Riesz transform of Lp(M0) then implies the boundedness of the Riesz transform of Lp(M).