Toeplitz算子和伪微分算子在调制空间之间的同构性质
Isomorphism properties of Toeplitz operators and pseudo-differential operators between modulation spaces
摘要：
我们研究了调制空间的提升性质，并构造了它们之间的显式同构。对于每个权函数$ω$和合适的窗函数$\fy $，Toeplitz算子（或定位算子）$\tp_\fy (ω)$是从$M^{p,q}_{(ω_0)}$到$M^{p,q}_{(ω_0/ω)}$的同构，用于每个$p,q \in [1,\infty ]$和任意权函数$ω_0$。这些方法涉及到Bony和Chemin的伪微分学以及某些伪微分算子符号类的Wiener代数性质。
英文摘要：
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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