Journal d'Analyse Mathématique

, 114:255

Isomorphism properties of Toeplitz operators and pseudo-differential operators between modulation spaces


    • Faculty of MathematicsUniversity of Vienna
  • Joachim Toft
    • Department of Computer Science, Mathematics and PhysicsLinnæus University

DOI: 10.1007/s11854-011-0017-8

Cite this article as:
Gröchenig, K. & Toft, J. JAMA (2011) 114: 255. doi:10.1007/s11854-011-0017-8


We investigate the lifting property of modulation spaces and construct explicit isomorphisms between them. For each weight function ω and suitable window function φ, the Toeplitz operator (or localization operator) Tpφ(ω) is an isomorphism from \(M_{({\omega _0})}^{p,q}\), onto \(M_{({\omega _0}/\omega )}^{p,q}\) for every p, q ∈ [1,∞] and arbitrary weight function ω0. The methods involve the pseudo-differential calculus of Bony and Chemin and the Wiener algebra property of certain symbol classes of pseudo-differential Operators.

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© Hebrew University Magnes Press 2011