The Riesz transform on a complete Riemannian manifold with Ricci curvature bounded from below

We study the Riesz transform and Hodge-Dirac operator on a complete Riemannian manifold with Ricci curvature bounded from below. We define the Hodge-Dirac operator ∏ on Lp(ΛTM) as the closure of d + d* on smooth, compactly supported k-forms for 1 < p < ∞. Given the boundedness of the Riesz transform on Lp(ΛTM), we show that ∏ is R-bisectorial on...

The Lp boundedness of the Riesz Transform

In this thesis we study theorems that will yield easier expressions for the Sobolev space W2,p.