Let b ∈ BMO(R~n) and let T be a standard Calderon-Zygmund singular integral operator. The commutator [b, T] generated by b and T is defined by [b, T]f(x) = b(x)Tf(x) - T(bf)(x). A celebrated result of Coifman, Rochberg, and Weiss states that the operator [b, T] is bounded on L~p(R~n) for 1 < p < ∞. Chanillo considered the similar question when the Calderon-Zygmund operator is replaced by the fractional integral operator. The main purpose of this paper is to generalize these results to the case of Herz spaces. Let us first introduce some notation.
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