Gaussian estimates and L ^p-boundedness of Riesz means

Abstract.

We show that suitable upper estimates of the heat kernel are sufficient to imply the L ^p boundedness of several families of operators associated with the Schrödinger group in various situations. This generalizes results by Sjöstrand and others in the Euclidean case, and by Alexopoulos in the case of Lie groups and Riemannian manifolds.