带变量核的分数次积分算子在加权Morrey空间上的有界性

Boundedness of fractional integral operators with variable kernels on weighted Morrey spaces

利用核函数Ω的性质,考虑了带变量核的分数次积分算子TΩ,α在加权Morrey空间上的有界性,证明了当Ω满足零阶齐次条件与消失距条件时,带变量核的分数次积分TΩ,α是从Lp,k(ωp,ωq)到Lq,kq/p(ωq)的有界算子,从而推广了以往非变量核的相关结果.

By using the properties of the functionΩ,the weighted boundedness results on the Morrey spaces were considered for the fractional integral operators TΩ,αwith variable kernels.It was showed that the TΩ,αwere bounded operators fromLp,k（ωp,ωq）to Lq,kq/p（ωq）when it met the zero order homogeneous conditions and vanishing moment condition,which extended no-variable kernel results that had been achieved in previous research.