Imaginary Powers of the Dunkl Harmonic Oscillator

In this paper we continue the study of spectral properties of the Dunkl harmonic oscillator in the context of a finite reflection group on $\mathbb R^d$ isomorphic to $\mathbb Z^d_2$. We prove that imaginary powers of this operator are bounded on $L^p$, $1<p<\infty$, and from $L^1$ into weak $L^1$.