In this paper we show how to use mollifiers to regularise functions relative to a set of Dunkl operators in R d with Coxeter-Weyl group W , multiplicity function k and weight function ω k. In particular for Ω a W-invariant open subset of R d , for ϕ ∈ D(R d) a radial function and u ∈ L 1 loc (Ω, ω k (x)dx), we study the Dunkl-convolution product u * k ϕ and the action of the Dunkl-Laplacian and the volume mean operators on these functions. The results are then applied to obtain an analog of the Weyl lemma for Dunkl-harmonic functions and to characterize them by invariance properties relative to mean value and convolution operators.