多线性Marcinkiewicz高阶交换子在变指数Herz-Morrey空间上的有界性

Boundedness of Higher Order Commutator of Multilinear Marcinkiewicz on Herz-Morrey Space with Variable Exponent

利用特征函数和空间分解原理对算子进行了估计。当指数满足p/n--n+α<0,nγi-αi<0时,证明了多线性Marcinkiewicz算子与有界平均振动(BMO)函数生成的高阶交换子在变指数Herz-Morrey空间上的有界性。该结果也是经典Marcinkiewicz交换子在变指数Herz-Morrey空间上的推广。

The characteristic function and the spatial decomposition principle were used to estimate operators.When the exponent satisfies p/n--n+α<0,nγi-αi<0,the boundedness of the high order commutator generated by multilinear Marcinkiewicz operator and bounded mean oscillation (BMO) function on Herz-Morrey space with variable exponent is proved. The results are also generalizations of the classical Marcinkiewicz commutator on Herz-Morrey space with variable exponent.