Integral Equations and Operator Theory

, Volume 48, Issue 4, pp 427–442

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 L2 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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