Riesz transforms for Dunkl Hermite expansions

In the present paper, we establish that Riesz transforms for Dunkl Hermite expansions introduced by Nowak and Stempak are singular integral operators with Hörmander's type condition. We prove that they are bounded on L^p(R^d,d_μκ)$L^p({\mathbb{R}}^d,d{\mu }_{\kappa })$ for 1<p<∞$1<p<\infty$ and from L¹(R^d,d_μκ)$L^1({\mathbb{R}}^d,d{\mu }_{\kappa })$ into L^1,∞(R^d,d_μκ)$L^{1,\infty }({\mathbb{R}}^d,d{\mu }_{\kappa })$.