Continuity and Schatten properties for pseudo-differential operators with symbols in quasi-Banach modulation spaces or Hörmander classes

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 $0$ and $1$. 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.

38 pages. Karlheinz Gröchenig 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 Hörmander-Weyl calculus. Sections 2 and 4 are modified. arXiv admin note: text overlap with arXiv:1404.0758

References in corpus (1)

• Gelfand-Shilov spaces, Structural and Kernel theorems

Cited by in corpus (2)

• Approximation property and nuclearity on mixed-norm $L^p$, modulation and Wiener amalgam spaces
• Schatten properties, nuclearity and minimality of shift invariant spaces