Abstract: The boundedness of multilinear Marcinkiewicz operators with variable kernels was studied on variable index Herz-Morrey spaces, which is also the generalization of classical Marcinkiewicz operators on variable index Herz-Morrey spaces. By using the eigenfunction and the space decomposition principle, the operator is divided into four parts in this paper, and then the operator is estimated one by one by using the size condition satisfied by the kernel functions. The boundedness of the operator on the variable index Herz-Morrey space is therefore obtained.

Key words: variable exponential Herz-Morrey space, multilinear Marcinkiewicz operator, boundedness