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

TL;DR

This paper establishes dimension-free bounds for Riesz transforms associated with the harmonic oscillator on -dimensional Euclidean space, providing explicit $L^p$ norm estimates that depend linearly on nd p.

Contribution

It provides explicit, dimension-independent $L^p$ bounds for Riesz transforms related to the harmonic oscillator, advancing understanding of their behavior in high-dimensional spaces.

Findings

Dimension-free $L^p$ bounds for Riesz transforms

Explicit estimates linear in nd p

Applicable to harmonic oscillator-related transforms

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