Original paper

Integral Equations and Operator Theory

, Volume 48, Issue 4, pp 427-442

First online:

Generalized Anti-Wick Operators with Symbols in Distributional Sobolev spaces

  • Paolo BoggiattoAffiliated withDipartimento di Matematica, Università di Torino Email author 
  • , Elena CorderoAffiliated withDipartimento di Matematica, Università di Torino
  • , Karlheinz GröchenigAffiliated withDepartment of Mathematics, University of Connecticut

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Abstract.

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 [20], [10], [5], [4], and [14].

Mathematics Subject Classification (2000).

47G30 35S05 46E35 47B10

Keywords.

Anti-Wick operator time-frequency localization operator modulation space Sobolev space Schatten class convolution relation