Some Sharp L2 Inequalities for Dirac Type Operators

We use the spectra of Dirac type operators on the sphere Sn to produce sharp L2 inequalities on the sphere. These operators include the Dirac operator on Sn, the conformal Laplacian and Paenitz operator. We use the Cayley transform, or stereographic projection, to obtain similar inequalities for powers of the Dirac operator and their inverses in Rn