Spectral Multipliers for Magnetic Schrödinger Operators

In this paper, we prove some spectral multiplier theorems for a self-adjoint operator H on Besov and Triebel–Lizorkin type spaces. This allows to give norm characterization of the perturbed Sobolev and Besov spaces associated with H. As an application, we obtain the local well posedness and uniqueness for the solutions to dispersive equations with certain magnetic potentials.