On the Continuity and Compactness of Pseudodifferential Operators on Localizable Hardy Spaces

Abstract

Listen

Translate article

In this paper we establish Sobolev type compact embedding theorems for Hormander classes of pseudodifferential operators $OpS^{-\alpha }_{1,\delta }$ on localizable Hardy space. Our work include new optimal boundedness results. As application, we obtain compact embeddings for compactly supported distributions with respect to the space variables in the nonhomogeneous localizable Hardy-Sobolev spaces.