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arXiv · 2208.02065

A Mikhlin--H\"ormander multiplier theorem for the partial harmonic oscillator

Xiaoyan Su·Ying Wang·Guixiang Xu
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Abstract

We prove a Mikhlin--H\"ormander multiplier theorem for the partial harmonic oscillator $H_{\textup{par}}=-\pa_\rho^2-\Delta_x+|x|^2$ for $(\rho, x)\in\R\times\R^d$ by using the Littlewood--Paley $g$ and $g^\ast$ functions and the associated heat kernel estimate. The multiplier we have investigated is defined on $\mathbb R \times \mathbb N$.

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Xiaoyan Su, Ying Wang, Guixiang Xu. 2022-08-03. A Mikhlin--H\"ormander multiplier theorem for the partial harmonic oscillator. https://arxiv.org/abs/2208.02065

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