多线性分数次积分及其极大算子在变指标Herz空间上的有界性  

BOUNDEDNESS OF FRACTIONAL MULTILINEAR SINGULAR INTEGRAL AND MAXIMAL OPERATOR ON VARIABLE EXPONENT HERZ SPACES

作　　者：殷露露 张婧 YIN Lu-lu;ZHANG Jing(School of Mathematics and Statistics,Yili Normal University,Yining 835000,China)

机构地区：[1]伊犁师范大学数学与统计学院,新疆伊宁835000

出　　处：《数学杂志》2020年第4期481-492,共12页Journal of Mathematics

基　　金：伊犁师范大学博士启动基金(2017YSBS09).

摘　　要：本文研究了多线性分数次积分算子TΩ,μA及其极大算子MΩ,μA在变指标空间上的有界性.利用变指标Lebesgue空间和Lipschitz空间的相关性质,获得了这两类算子分别在变指标Herz空间和变指标Herz-Morrey空间上的有界性.这一结果推广了这两类算子在变指标Lebesgue空间上有界性的结论.In this paper,we study the the boundedness of fractional multilinear integral operator TΩ,μA and maximal operator MΩ,μA on variable exponent spaces.By using some properties of variable exponent Lebesgue space and Lipschitz space,it is additionally obtain the boundedness of fractional multilinear integral operators on variable exponent Herz spaces and variable exponent Herz-Morrey spaces,which generalize the main theorems for the boundedness of fractional multilinear integral operators on variable exponent Lebesgue space.

关 键 词：粗糙核 多线性分数次积分算子 多线性分数次极大算子 变指标Herz空间 变指标Herz-Morrey空间 

分 类 号：O174.2[理学—数学]