A limiting absorption principle for high-order Schrödinger operators in critical spaces

Abstract

In this paper, we prove a limiting absorption principle for high-order Schrödinger operators with a large class of potentials that generalize some results by Ionescu and Schlag. Two key tools we use in this paper are the Stein–Tomas theorem in Lorentz spaces and a sharp trace lemma given by Agmon and Hörmander.