非二倍测度下截口上的分数次积分算子的有界性  

Boundedness of fractional integral operators associated to the sections for non-doubling measures

作　　者：孙建国[1] 陶双平[1] 

机构地区：[1]西北师范大学数学与信息科学学院,甘肃兰州730070

出　　处：《西北师范大学学报（自然科学版）》2008年第5期17-19,共3页Journal of Northwest Normal University(Natural Science)

基　　金：甘肃省教育厅科研基金资助项目(0701-15)

摘　　要：研究非二倍测度下截口上的分数次积分Iαf(x)=∫Rn(1/d(x,y)n-α)f(y)dμ(y),这里0<α<n,d(x,y)为截口上的拟度量.证明了Iα是从Lp(Rn)到Lorentz空间Lq,∞(Rn)的有界算子,同时还证明了增长条件μ(S(x,r))≤Crn,x∈Rn,r>0是上述结论成立的必要条件.The fractional integral operators associated to the sections for non-doubling measures are considered,which is defined by Iαf(x)=∫Rn(1/d(x,y)n-α)f(y)dμ(y),where 0<α<n,d(x,y) is a quasi-metric associated to the sections.It is obtained that Iα is a bounded operator from Lp(Rn) into the Lorentz space Lq,∞(Rn).And also it is proved that the growing condition μ(S(X,r))≤Crn,x∈Rn,r>0 is a necessary condition for the result.

关 键 词：分数次积分 有界算子 非二倍测度 截口 

分 类 号：O177[理学—数学]