齐次核的Hilbert型级数不等式取最佳常数因子的充要条件  

A Necessary and Sufficient Condition of that Hilbert Type Series Inequality with Homogeneous Kernel Has the Best Constant Factor

作　　者：洪勇[1] 温雅敏[1] HONG Yong WEN Yamin(College of Mathematics and Statistics, Guangdong University of Finance and Economics, Guangzhou 510320, China.)

机构地区：[1]广东财经大学数学与统计学院,广州510320

出　　处：《数学年刊（A辑）》2016年第3期329-336,共8页Chinese Annals of Mathematics

基　　金：国家自然科学基金(No.61300204);广东省自然科学基金(No.S2012010010376);广州市科技计划项目(No.2010GN-C021)的资助

摘　　要：利用实分析技巧及权函数方法,解决了具有齐次核的Hilbert型级数不等式取最佳常数因子的充要条件,并讨论其在算子理论中的应用.By using the technic of real analysis and the way of weight functions,a necessary and sufficient condition of that Hilbert type series inequality with homogeneous kernel has the best constant is obtained.Its appUcations in operator theory are considered.

关 键 词：Hilbert型级数不等式 最佳常数因子 充要条件 有界算子 

分 类 号：O178[理学—数学]