多线性Marcinkiewicz算子在变指数Herz-Morrey空间上的有界性

The boundedness of multilinear Marcinkiewicz operator in variable index Herz-Morrey space

研究了多线性Marcinkiewicz算子在变指数Herz-Morrey空间上的有界性,也是经典Marcinkiewicz算子在变指数Herz-Morrey空间上的推广.使用特征函数和空间分解原理,将算子分为4个部分,核函数所满足的尺寸条件,对算子进行估计,得到算子在变指数Herz-Morrey空间上的有界性.

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.