For \(q\in (2,\infty )\) , let \(V_q K\) be the variation operator of a family truncated operators of a singular integral K and a space \((\mathbb {R}^{N},\left\| \cdot \right\| ,\mu )\) in the Dunkl setting, where the integral kernel has estimations involving two different metrics, namely, the Euclidean and the Dunkl (orbit) metrics. Under the assumption that \(V_q K\) is bounded on \(L^{p_0}(\mu )\) for some \(p_0 \in (1,\infty )\) , we obtain the boundedness of \(V_q K\) on \(L^p(\mu )\) for \(1<p<\infty \) , from \(L^1(\mu )\) to \(L^{1,\infty }(\mu )\) , and from the space of bounded measurable functions with compact support \(L_0^{\infty }(\mu )\) to \(BMO(\mu )\) . These results are also true for oscillation operators.
