非倍测度空间上分数次Hardy算子的有界性  

Boundedness of Fractional Hardy Operators on Spaces with Nondoubling Measures

作　　者：宋帆 李亮[1] SONG Fan;LI Liang(College of Mathematics and Statistics,Yili Normal University,Yining Xinjiang 835000,China)

机构地区：[1]伊犁师范学院数学与统计学院,新疆伊宁835000

出　　处：《长春师范大学学报》2018年第4期1-5,共5页Journal of Changchun Normal University

基　　金：国家自然科学基金资助项目"非齐型测度空间上多参数奇异积分算子研究"(11561067);新疆自然科学基金资助项目"亚音速管道流与跨音速激波机制研究"(2016D01C379)

摘　　要：本文在底空间R^d的测度仅满足一类增长性条件的假设下,引入了一类分数次Hardy算子H_β和H_β~*的定义,并讨论了该算子在Herz空间与Lebesgue空间上的有界性,结论推广了测度μ是经典欧氏测度时的情形。Letμbe a Radon measure on Rd only satisfying the growth condition,we firstly introduced the definition of fractional Hardy operators.Moreover,the boundedness of these operators on Herz space and Lebesgue spaces are obtained in this paper.It is should be noted that the conclusion extend the case under Euclid measures.

关 键 词：分数次Hardy算子 HERZ空间 非倍测度 有界性 

分 类 号：O174.2[理学—数学]