Pseudodifferential Operators, Rellich-Kondrachov Theorem and Hardy-Sobolev Spaces
arXiv:1704.00017
Abstract
We will present versions of the Rellich-Kondrachov theorem for pseudo-differential operators acting on localizable Hardy spaces. One of the techniques includes boundedness properties for pseudodifferential operators with symbols in the Hörmander class, that might be of interest in his own right, extending results previously obtained by Goldberg, Alvarez and Hounie, Taylor - among others. As application, we obtain compact embedding results for distributions in nonhomogeneous localizable Hardy-Sobolev spaces.
arXiv commentThere is an error in the proof of theorem B. The conclusion of the theorem is correct, but the argument used is not