English

Continuity and Schatten properties for pseudo-differential operators with symbols in quasi-Banach modulation spaces or H\"ormander classes

Functional Analysis 2016-05-02 v4

Abstract

We establish continuity and Schatten-von Neumann properties for matrix operators with matrices satisfying mixed quasi-norm estimates. These considerations also include the case when the Lebesgue and Schatten parameters are allowed to stay between 00 and 11. We use the results to deduce continuity and Schatten-von Neumann properties for pseudo-differential operators with symbols in a broad class of modulation spaces.

Keywords

Cite

@article{arxiv.1406.3820,
  title  = {Continuity and Schatten properties for pseudo-differential operators with symbols in quasi-Banach modulation spaces or H\"ormander classes},
  author = {Joachim Toft},
  journal= {arXiv preprint arXiv:1406.3820},
  year   = {2016}
}

Comments

38 pages. Karlheinz Gr\"ochenig was one of the authors in the first version. It was then decided that he will not be one of the authors of the paper. A new Subsection 1.8 is included which informs about H\"ormander-Weyl calculus. Sections 2 and 4 are modified. arXiv admin note: text overlap with arXiv:1404.0758