Propagation Theorems for Some Classes of Pseudo-Differential Operators

We study continuity properties of the boundary values of the resolvent of perturbations of certain pseudo-differential operators by using recent versions of the conjugate operator method. Our results are optimal on the H¨older]Zygmund scale. In particular, three physical situations are included, namely relativistic and non-relativistic Schr¨odinger operators and the Stark effect hamiltonian. We allow a large class of perturbations by giving an ‘‘optimal’’ compromise between regularity and decay at infinity.