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

Harmonic analysis operators in the rational Dunkl settings