A Mikhlin--Hörmander multiplier theorem for the partial harmonic oscillator

Xiaoyan Su, Ying Wang, Guixiang Xu

We prove a Mikhlin--Hörmander multiplier theorem for the partial harmonic oscillator $H_{\textup{par}}=-\pa_ρ^2-Δ_x+|x|^2$ for $(\rho ,x)\in \mathbb{R}\times {\mathbb{R}}^d$ by using the Littlewood--Pale…