多线性分数次积分算子在变指数Herz-Morrey空间上的有界性

Boundedness of Multilinear Fractional Integral Operators on Herz-Morrey Spaces with Variable Exponent

主要研究多线性分数次积分算子Iα(m)在变指数Herz-Morrey空间的乘积空间MKσ1,λ1q1,p1(·)(Rn)×MKσ2,λ2q2,p2(·)(Rn)×…×MKσm,λmqm,pm(·)(Rn)上的有界性.即经典分数次积分算子在Herz-Morrey空间上有界性的多线性形式的推广.主要使用特征函数将分数次积分算子分解,逐个进行估计,最终得到Iα(m)在变指数Herz-Morrey空间的乘积空间的有界性.

This study attempted to prove the boundedness of multilinear fractional integral operators from the product of Herz-Morrey spaces with variable exponent MKq1,p1（·）^σ1,λ1（R^n）×MKq2,p2（·）^σ2,λ2（R^n）×…×MKqm,pm（·）^σm,λm（R^n）. It is an extension of the boundedness of fractional integral operators to multilinear cases. The characteristic function was used to decompose the fractional integral operators, estimate every part of the decomposition and obtain the boundedness of Iα（m）on the product of variable exponent Herz-Morrey spaces.