Generalized Anti-Wick Operators with Symbols in Distributional Sobolev spaces
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Generalized Anti-Wick operators are introduced as a class of pseudodifferential operators which depend on a symbol and two different window functions. Using symbols in Sobolev spaces with negative smoothness and windows in so-called modulation spaces, we derive new conditions for the boundedness on L 2 of such operators and for their membership in the Schatten classes. These results extend and refine results contained in , , , , and .
Mathematics Subject Classification (2000).47G30 35S05 46E35 47B10
Keywords.Anti-Wick operator time-frequency localization operator modulation space Sobolev space Schatten class convolution relation
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