, Volume 114, Issue 1, pp 255-283
Date: 21 Sep 2011

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

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Abstract

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) Tp φ (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 ω 0. The methods involve the pseudo-differential calculus of Bony and Chemin and the Wiener algebra property of certain symbol classes of pseudo-differential Operators.

K.G. was supported by the Marie-Curie Excellence Grant. MEXT-CT-2004-517154