Functions of the Laplace Operator on Manifolds with Lower Ricci and Injectivity Bounds

Recent work of G. Mauceri, S. Meda, and M. Vallarino produces L ^p estimates on a natural class of functions of the Laplace–Beltrami operator on a Riemannian manifold M, under fairly weak geometrical hypotheses, namely lower bounds on its injectivity radius and Ricci tensor, but with an auxiliary decay hypothesis on the heat semigroup. We sharpen this result by removing the decay hypothesis.