Dimension-free estimates for Riesz transforms related to the harmonic oscillator
Volume 165 / 2021
Colloquium Mathematicum 165 (2021), 139-161
MSC: 42C10, 42A50, 33C50.
DOI: 10.4064/cm8047-8-2020
Published online: 19 December 2020
Abstract
We study $L^p$ bounds for two kinds of Riesz transforms on $\mathbb R ^d$ related to the harmonic oscillator. We pursue an explicit estimate of their $L^p$ norms that is independent of the dimension $d$ and linear in $\max (p, p/(p-1))$.
