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Schatten Properties for Pseudo-Differential Operators on Modulation Spaces

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Pseudo-Differential Operators

Part of the book series: Lecture Notes in Mathematics ((LNMCIME,volume 1949))

Abstract

Let M (ω) p,q be the modulation space with parameters p, q and weight function ω. Also let t ∈ R and assume that a ∈ M (ω) p,q. We establish sufficient and necessary conditions on p, q ∈ [1, ∞], ω1, ω2, and ω in order to the pseudo-differential operator a t (x,D) should be a Schatten–von Neumann operator from M (ω1) 2,2, to M (ω2) 2,2 of certain order.

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Authors and Affiliations

  1. Department of Mathematics and Systems Engineering, Växjö University, Vejdes plats 6,7, 35195, Växjö, Sweden

    J. Toft

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  1. J. Toft
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Editor information

Editors and Affiliations

  1. Dipartimento di Matematica, Universitá di Torino, Via Carlo Alberto 10, 10123, Torino, Italy

    Luigi Rodino

  2. Department of Mathematics and Statistics, York University, Keele Street 4700, M3J 1P3, Toronto, Ontario, Canada

    M. W. Wong

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Toft, J. (2008). Schatten Properties for Pseudo-Differential Operators on Modulation Spaces. In: Rodino, L., Wong, M.W. (eds) Pseudo-Differential Operators. Lecture Notes in Mathematics, vol 1949. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-68268-4_5

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