  Let $L_k=-\Delta_k+V$ be the Dunk- Schr\"{o}dinger operators, where
$\Delta_k=\sum_{j=1}^dT_j^2$ is the Dunkl Laplace operator associated to the
dunkl operators $T_j$ on $\mathbb{R}^d$ and $V$ is a nonnegative potential
function.
  In the first part of this paper we introduce the Riesz transform $R_j= T_j
L_k^{-1/2}$ as an $L^2$- bounded operator and we prove that is of weak type
$(1,1)$ and then is bounded on $L^p(\mathbb{R}^d,d\mu_k(x))$ for $1<p\leq 2$.
The second pat is devoted to the $L^p$ smoothing of the semigroup generated by
$L_k$, when $V$ belongs to the standard Koto class.
