  In this paper we study harmonic analysis operators in Dunkl settings
associated with finite reflection groups on Euclidean spaces. We consider
maximal operators, Littlewood-Paley functions, $\rho$-variation and oscillation
operators involving time derivatives of the heat semigroup generated by Dunkl
operators. We establish the boundedness properties of these operators in
$L^p(\mathbb R^d,\omega _\mathfrak K)$, $1\leq p < 1$, Hardy spaces, BMO and
BLO-type spaces in the Dunkl settings. The study of harmonic analysis operators
associated to reflection groups need different strategies from the ones used in
the Euclidean case since the integral kernels of the operators admit
estimations involving two different metrics, namely, the Euclidean and the
orbit metrics. For instance, the classical Calder\'on-Zygmund theory for
singular integrals does not work in this setting.
