L^p-Analysis of the Hodge–Dirac Operator Associated with Witten Laplacians on Complete Riemannian Manifolds.

We prove R-bisectoriality and boundedness of the (Formula presented.)-functional calculus in (Formula presented.) for all (Formula presented.) for the Hodge–Dirac operator associated with Witten Laplacians on complete Riemannian manifolds with non-negative Bakry–Emery Ricci curvature on k-forms.

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...