  We consider several harmonic analysis operators in the multi-dimensional
context of the Dunkl Laplacian with the underlying group of reflections
isomorphic to $\mathbb{Z}_2^n$ (also negative values of the multiplicity
function are admitted). Our investigations include maximal operators,
$g$-functions, Lusin area integrals, Riesz transforms and multipliers of
Laplace and Laplace-Stieltjes transform type. Using the general
Calder\'on-Zygmund theory we prove that these objects are bounded in weighted
$L^p$ spaces, $1<p<\infty$, and from $L^1$ into weak $L^{1}$.
