Pseudo-Differential Operators and Related Topics

doi:10.1007/3-7643-7514-0

2006

DOI: 10.1007/3-7643-7514-0

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Pseudo-Differential Operators and Related Topics

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2010

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Mixed modulation spaces and their application to pseudodifferential operators

Bishop

2010

Journal of Mathematical Analysis and Applications

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This paper uses frame techniques to characterize the Schatten class properties of integral operators. The main result shows that if the coefficients { k, Φ m,n } of certain frame expansions of the kernel k of an integral operator are in 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.

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Mixed modulation spaces and their application to pseudodifferential operators

Bishop

2010

Journal of Mathematical Analysis and Applications

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Pseudo-Differential Operators and Related Topics

Cited by 1 publication

References 129 publications

Mixed modulation spaces and their application to pseudodifferential operators

Mixed modulation spaces and their application to pseudodifferential operators

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