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

2014/06/15 by Toft, Joachim
#FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1406.3820

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.

Related

• Continuity of Gevrey-Hörmander pseudo-differential operators on modulation spaces
• Pseudo-differentialoperators on Orlicz modulation spaces
• Quasi-Banach Schatten-von Neumann properties in Weyl-Hörmander calculus
• Anisotropic Gevrey-Hörmander pseudo-differential operators on modulation spaces
• A counterexample for boundedness of pseudo-differential operators on modulation spaces