论文标题
Mikhlin-Hörmander乘数定理，用于部分谐波振荡器
A Mikhlin--Hörmander multiplier theorem for the partial harmonic oscillator
论文作者
论文摘要
我们证明了部分谐波振荡器的Mikhlin-Hörmander乘数定理$ h _ {\ textup {par}} = - \ \pa_p_ρ^2- x-δ_x+| x | x |^2 $ for $（ρ，ρ，x）内核估计。我们研究的乘数是在$ \ Mathbb R \ Times \ Mathbb n $上定义的。
We prove a Mikhlin--Hörmander multiplier theorem for the partial harmonic oscillator $H_{\textup{par}}=-\pa_ρ^2-Δ_x+|x|^2$ for $(ρ, x)\in\R\times\R^d$ by using the Littlewood--Paley $g$ and $g^\ast$ functions and the associated heat kernel estimate. The multiplier we have investigated is defined on $\mathbb R \times \mathbb N$.
