调制空间上的Hermite乘子
Hermite Multipliers on Modulation Spaces
摘要：
研究了调制空间$M^{p,q}(\mathbb R^d)$上与Hermite算子$H=-Δ+ |x|^2$相关的乘子.我们证明了算子$m(H)$在$m,$上的标准条件下在$M^{p,q}(\mathbb R^d)$上有界，从而为选择合适的$p$和$q$提供了依据.作为应用，我们指出在调制空间中初始数据的$H$的自由波和薛定谔方程的解将始终保持在同一调制空间中.我们还指出与$H$相关的Riesz变换在某些调制空间上是有界的。
英文摘要：
We study multipliers associated to the Hermite operator $H=-Δ+ |x|^2$ on modulation spaces $M^{p,q}(\mathbb R^d)$. We prove that the operator $m(H)$ is bounded on $M^{p,q}(\mathbb R^d)$ under standard conditions on $m,$ for suitable choice of $p$ and $q$. As an application, we point out that the solutions to the free wave and Schrödinger equations associated to $H$ with initial data in a modulation space will remain in the same modulation space for all times. We also point out that Riesz transforms associated to $H$ are bounded on some modulation spaces.
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