(untitled) (Journal of Mathematical Study, 2020)
On the real line, the Dunkl operators D_ u(f)(x):=d f(x)dx + (2 u+1) f(x) - f(-x)2x, x R, u -12 are differential-difference operators associated with the reflection group Z_2 on R, and on the R^d the Dunkl operators {D_k,j}_j=1^d are the differential-difference operators associated with the reflection group Z_2^d on R^d. In this paper, in the setting R we show that b BMO(R,dm_ u) if and only if the maximal commutator M_b, u is bounded on Orlicz spaces L_Φ(R,dm_ u). Also in the setting R^d we show that b BMO(R^d,h_k^2(x) dx) if and only if the maximal commutator M_b,k is bounded on Orlicz spaces L_Φ(R^d,h_k^2(x) dx).