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

Shahla Molahajloo, Götz E. Pfander

Published 2015-04-22Version 1

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.