讨论了由核函数满足具有某类Dini条件的Marcinkiewicz积分μΩ力及函数b∈Lipβ(R^n)生成的交换子μ^mΩ,b的性质.证明了Marcinkiewicz积分交换子μ^mΩ,b在Hardy型空间H^pbm,s(R^n)上有界,也在Herz型Hardy空间HbmK^α,pq(R^n)上有界.
In this paper, the properties of commutators μ^mΩ,b are studied, which are generalized by the Marcinkiewicz operator μΩ with the kernel satisfying center Dini condition and the function b ∈ Lipβ(R^n). The boundedness of μ^mΩ,b on the space of Hardy type Hpbm,s(R^n) and that on the Herz-type Hardy space Hbm,K^α,pq(R^n) are established.