多线性奇异积分和分数次积分的有界性  

The Boundedness of Mulitilinear Singular and Fractional Integrals

作　　者：牛采银[1] 

机构地区：[1]淮阴工学院计算科学系,江苏淮安223003

出　　处：《淮阴工学院学报》2007年第5期10-14,共5页Journal of Huaiyin Institute of Technology

摘　　要：奇异积分和分数次积分是近代调和分析中的重要算子,因而研究它在各种空间的有界性就很有意义.丁勇等人证明了多线性奇异积分与分数次积分从Lp(Rn)到Lq(Rn)的有界性,笔者把他的结果推广到了Helz空间,主要讨论了多线性奇异和分数次积分从.qα,1p(Rn)到.Kαq2,p(Rn)的有界性,使得关于多线性奇异和分数次积分的有界性理论更加完善.The singular integral and the fractional integral are very important operators. So it is very significant to research their boundedness in various function spaces. Ding yong and so on have proved the boundedness of mulitilinear singular and fractional intergrals from L^p （ R^n ） to L^q （ R^n ）. In this paper the anther generalised his results to the Herz space, and studied the boundedness of this operater from.q1^α,p （ R^n ） to Kq2^α,p （ R^n ） . The shows make the boundedness theory of mulitilinear singular and fractional integrals more complete.

关 键 词：多线性 奇异和分数次积分 HERZ空间 

分 类 号：Q175.5[生物学—水生生物学]