Boundedness of Pseudo-Differential Operators on L^p, Sobolev and Modulation Spaces

¹ Department of Mathematics and Statistics, Queen’s University, Kingston, Ontario K7L3N6, Canada
² School of Engineering and Science, Jacobs University, 28759 Bremen, Germany

^∗ Corresponding author. E-mail: molahajloo@mast.queensu.ca

Abstract

We introduce new classes of modulation spaces over phase space. By means of the Kohn-Nirenberg correspondence, these spaces induce norms on pseudo-differential operators that bound their operator norms on L^p–spaces, Sobolev spaces, and modulation spaces.