This is an announcement for the paper "Mixed modulation spaces and their application to pseudodifferential operators" by Shannon Bishop.

Abstract: This paper uses frame techniques to characterize the Schatten class properties of integral operators. The main result shows that if the coefficients of certain frame expansions of the kernel of an integral operator are in ( \ell^{2,p} ), then the operator is Schatten p-class. As a corollary, we conclude that if the kernel or Kohn-Nirenberg symbol of a pseudodifferential operator lies in a particular mixed modulation space, then the operator is Schatten p-class. Our corollary improves existing Schatten class results for pseudodifferential operators and the corollary is sharp in the sense that larger mixed modulation spaces yield operators that are not Schatten class.

Archive classification: math.FA math.CA

Mathematics Subject Classification: 35S05 (Primary) 42C15, 47B10 (Secondary)

Remarks: To be published in Journal of Mathematical Analysis and Applications

The source file(s), genmodshortD3.tex: 53295 bytes, is(are) stored in gzipped form as 0908.3420.gz with size 13kb. The corresponding postcript file has gzipped size 108kb.

Submitted from: sbishop@math.gatech.edu

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