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Generalized Anti-Wick Operators with Symbols in Distributional Sobolev spaces

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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].

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Authors and Affiliations

  1. Dipartimento di Matematica, Università di Torino, Via C. Alberto 10, Torino, 10123, Italy

    Paolo Boggiatto & Elena Cordero

  2. Department of Mathematics, University of Connecticut, Storrs, CT, 06269-3009, USA

    Karlheinz Gröchenig

Authors
  1. Paolo Boggiatto
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  2. Elena Cordero
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  3. Karlheinz Gröchenig
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Correspondence to Paolo Boggiatto.

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Boggiatto, P., Cordero, E. & Gröchenig, K. Generalized Anti-Wick Operators with Symbols in Distributional Sobolev spaces. Integr. equ. oper. theory 48, 427–442 (2004). https://doi.org/10.1007/s00020-003-1244-x

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  • DOI: https://doi.org/10.1007/s00020-003-1244-x

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