Boundedness and compactness arguments in the Hörmander spaces for linear pseudo-differential operators are considered. The symbol of is assumed to obey appropriate temperate criteria, which guarantee that maps the Schwartz class into itself and,that the formal transpose exists. A characterization for the boundedness of the operator is obtained. A sufficient condition for the boundedness of the operator with is established as well. Finally, the compactness of the continuous extension of is studied, where is an open bounded set in and where is (essentially) the completion of with respect to the -norm.
Cite this article
Jouko Tervo, On -Boundedness and Compactness of Linear Pseudo-Differential Operators. Z. Anal. Anwend. 7 (1988), no. 1, pp. 41–56