PROPAGATION THEOREMS FOR SOME CLASSES OF PSEUDODIFFERENTIAL-OPERATORS

We study continuity properties of the boundary values of the resolvent of perturbations of certain pseudo-differential operators by using re cent versions of the conjugate operator method. Our results are optima l on the Holder-Zygmund scale. In particular, three physical situation s are included, namely relativistic and non-relativistic Schrodinger o perators and the Stark effect hamiltonian. We allow a large class of p erturbations by giving an ''optimal'' compromise between regularity an d decay at infinity. (C) 1997 Academic Press.