Abstract
In this paper we establish Sobolev type compact embedding theorems for Hörmander 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.
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Acknowledgment
We wish to thank Prof. Jorge Hounie (Universidade Federal de São Carlos) and the referee for helpful discussions and suggestions concerning this work.
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Work supported in part by CNPq (grant number 308826/2018-3, 311430/2018-0 and 409306/2016-9) and FAPESP (grant numbers 2018/14316-3, 2019/04995-3 and 2018/15484-7).
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Hoepfner, G., Kapp, R. & Picon, T. On the Continuity and Compactness of Pseudodifferential Operators on Localizable Hardy Spaces. Potential Anal 55, 491–512 (2021). https://doi.org/10.1007/s11118-020-09866-0
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DOI: https://doi.org/10.1007/s11118-020-09866-0