2 papers
math.AP2022
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 by using the Littlewood--Pale…
math.AP2022
Riesz transforms and Sobolev spaces associated to the partial harmonic oscillator
Xiaoyan Su, Ying Wang, Guixiang Xu
In this paper, our goal is to establish the Sobolev space associated to the partial harmonic oscillator. Based on its heat kernel estimate, we firstly give the definition of the fr…