Dimension-free estimates for Riesz transforms related to the harmonic oscillator

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 $\max (p,p/(p-1))$.

25 pages

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