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中文摘要：
设（x,d,μ）是一个满足上双倍条件和几何双倍条件的度量测度空间.证明了Marcinkiewicz积分M与Lip_β（μ）函数b生成的交换子M_b的（Lp（μ）,Lq（μ））型和（L1（μ）,Ln/（n-β）·∞（μ））型不等式.得到交换子M_b是从Hardy空间H1（μ）到Ln/（n-β）（μ）上有界的.
英文摘要：
Let（x,d,μ） be a measure space satisfying the upper doubling condition and the geometrically doubling condition,the inequalities of type（Lp（μ）,Lq（μ）） and type（L1（μ）,Lπ/（n-β）·∞（μ）） are obtained for the Marcinkiewicz commutator M_b generated by the Marcinkiewicz integral operator M and the Lipβ（μ） function b.It was shown that the commutator M_b is bounded from Hardy spaces H1（μ） into the spaces Ln/（n-β）（μ）.
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