Spectral multipliers and wave propagation for Hamiltonians with a scalar potential

Abstract

We extend several fundamental estimates regarding spectral multipliers for the free Laplacian on R3 to the case of perturbed Hamiltonians of the form −Δ+V, where V is a scalar real-valued potential.In this paper, we prove resolvent estimates, a dispersive bound for the perturbed wave propagator, Mihlin multiplier and fractional integration bounds, and the full range of wave equation Strichartz estimates, under optimal or almost optimal scaling-invariant conditions on the potential and on the spectral multipliers themselves.