Minor Oral: "Boundedness of the Riesz Transforms on Complete Noncompact Riemannian Manifolds with Nonnegative Ricci Curvature"

Abstract: It is a well-known classical result that the Riesz transforms are bounded from L^p(R^n) to L^p(R^n) for all p in (1,infinity). More recently, the Riesz transforms were defined in the more general setting of a Riemannian Manifold  and similar boundedness properties were investigated. In 1987, Bakry proved that if M is a complete noncompact Riemannian manifold with nonnegative Ricci curvature, then the Riesz transforms are bounded from L^p(M) to L^p(M) for all p in (1,infinty). We will discuss Bakry's proof in this talk.

Host: Brett Wick