Oscillation inequalities for Carleson--Dunkl operator

In this paper, we establish estimates for the oscillation seminorm for the so-called Carleson--Dunkl operator on weighted Lᵖ(R,w(x)|x|2α+1 dx) spaces with power weights w(x)=|x|^β. As a result, we obtain oscillation estimates for the standard Carleson operator on Lradᵖ(Rⁿ,|x|^β dx). As a byproduct, we obtain the 'generalization' of the Rubio de Francia transference principle for radial multipliers.