用核函数$\text{It}\mathrm{\Omega }(x,z)$的性质,讨论了变量核~Marcinkiewicz~积分算子${\mu }_{\text{It}\mathrm{\Omega }}(f)$与$BMO({\text{bm}R}^n)$函数$b$生成的交换子$\text{Extra close brace or missing open brace}$的有界性,证明了当$\text{It}\mathrm{\Omega }(x,z)\in L^{\mathrm{\infty }}({\text{bm}R}^n){\text{timesL}}^r(S^{n-1})$ $(r\ge 1)$时${\mu }_{\text{It}\mathrm{\Omega },b}(f)$是齐次~Morrey-Herz
 空间$M{\dot{K}}_{p,q}^{\alpha ,\lambda }({\text{bm}R}^n)$上的有界算子, 从而推广了以往非变量核的结果.

By using the properties of the kernel function $\text{It}\mathrm{\Omega }(x,z)$, the boundedness of commutator ${\mu }_{\text{It}\mathrm{\Omega },b}(f)$ is considered, which is generated by a $\mathrm{B}\mathrm{M}\mathrm{O}({\text{bm}R}^n)$ function $b$ and the Marcinkiewicz integral operator ${\mu }_{\text{It}\mathrm{\Omega }}(f)$ with variable kernel. It is proved that ${\mu }_{\text{It}\mathrm{\Omega },b}$ is bounded on the Homogeneous Morrey-Herz spaces $M{\dot{K}}_{p,q}^{\alpha ,\lambda }({\text{bm}R}^n)$ as $\text{It}\mathrm{\Omega }(x,z)\in L^{\mathrm{\infty }}({\text{bm}R}^n)\times L^r(S^{n-1})$ $(r\ge 1)$, to generalize the previous non variable kernel results.