Isomorphism properties of Toeplitz operators and pseudo-differential operators between modulation spaces
We investigate the lifting property of modulation spaces and construct explicit isomorpisms between them. For each weight function $ω$ and suitable window function $\fy $, the Toeplitz operator (or localization operator) $\tp_\fy (ω)$ is an isomorphism from $M^{p,q}_{(ω_0)}$ onto $M^{p,q}_{(ω_0/ω)}$ for every $p,q \in [1,\infty ]$ 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.
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