变量核分数次积分交换子在Morrey空间上的加权估计

Weighted estimation of variable kernel fractional integral commutator in Morrey spaces

利用分数次积分在L^p空间的性质,证明了当核函数Ω(x,z)满足一定条件时,带变量核的分数次积分算子与Lipschitz函数b生成的交换子T^b Ω,a是从L^p,k(ω^p,ω^q)到L^q,kq/p(ω^q)的有界算子,从而推广了以往非变量核的相关结果。

Using the properties of fractional integral in Lpspace,it is proved that when Ω(x,z) meets certain conditions, the commutator T^b Ω, a generated by fractional integral operator T Ω,a with variable kernel and Lipschitz function b is a bounded operator from L^p,k(ω^p ,ω^q) to L^q,kq/p (ω^q), which generalizes the previous results of non - variable kernel.