Spectral multipliers III: Endpoint bounds, intertwining operators, and twisted Hardy spaces

Abstract

We extend several fundamental estimates regarding spectral multipliers for the free Laplacian on ${\mathbb{R}}^3$ to the case of perturbed Hamiltonians of the form $H=-\hat{I}”+V$, where $V$ is a scalar real-valued potential. Results include sharp bounds for Mihlin multipliers, partial confirmation for a conjecture made in [BeGo3] about intertwining operators, a characterization of the twisted Hardy spaces that correspond to these perturbed Hamiltonians, Strichartz estimates, and maximum principles.

38 pages