在本文中，證明了 Marcinkiewicz 積分交換子 $mu^m_{Omega,b}$ 是從原子Hardy空間 $H^p_{b^m}(omega )$ 到 $L^p_omega (Bbb{R}^n)$, $max{n/(n+1/2),n/(n+alpha)}<p<1$ 加權有界的 ，其中 $omega$ 是 Muckenhoupt 權函數。 In this paper, we prove that the commutator $mu^m_{Omega,b}$ of the marcinkiewicz integral $mu^m_{Omega}$ is a bounded operator from a class of atomic-Hardy spaces $H^p_{b^m}(omega)$ to $L^p_{omega}(Bbb{R}^n)$ for $max{ n/(n+1/2), n/(n+alpha)}<p<1$, where $omega $ is a Muckenhoupt weight.
