Integral Equations and Operator Theory

, Volume 48, Issue 4, pp 427–442 | Cite as

Generalized Anti-Wick Operators with Symbols in Distributional Sobolev spaces

  • Paolo Boggiatto
  • Elena Cordero
  • Karlheinz Gröchenig
Original paper

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 

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Copyright information

© Birkhäuser-Verlag 2004

Authors and Affiliations

  • Paolo Boggiatto
    • 1
  • Elena Cordero
    • 1
  • Karlheinz Gröchenig
    • 2
  1. 1.Dipartimento di MatematicaUniversità di TorinoTorinoItaly
  2. 2.Department of MathematicsUniversity of ConnecticutStorrsUSA

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