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 $\max(p, p/(p-1))$.
Riesz Transforms and Spectral Multipliers of the Hodge-Laguerre Operator
Hörmander condition for pseudo-multipliers associated to the harmonic oscillator
The property $\log(f) \in BMO(\mathbb R^n)$ in terms of Riesz transforms
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