Let b ∈ BMO(Rn) and T be the Calderón–Zygmund singular integral operator. The commutator [b,T ] generated by b and T is defined as [b,T ]( f )(x) = b(x)T ( f )(x)−T (b f )(x). By using a classical result of Coifman et al [8], we know that the commutator [b,T ] is bounded on Lp(Rn) for 1 < p < ∞. Chanillo [1] proves a similar result when T is replaced by the fractional integral operator. However...