摘要
参数满足什么条件时, Hilbert型级数不等式Σ^∞n=1Σ^∞m=1K(m,n)ambn≤M(Σ^∞m=1m^αa^p m )^1/p(Σ^∞n=1n^βb^qn )^1/q能够成立?而当Hilbert型级数不等式成立时,其常数因子又在什么条件下是最佳的?最佳常数因子的表达式是什么?这些问题的研究无疑是具有重要意义的.利用实分析的技巧及权函数方法,对具有齐次核的Hilbert型级数不等式的形式结构及参数关系进行了分析研究,得到其成立的充分必要条件和最佳常数因子的表达式.最后讨论了其结果在算子理论中的一些应用.
What conditions should the parameters satisfy for Hilbert’s type series inequalityΣ^∞n=1Σ^∞m=1K(m,n)ambn≤M(Σ^∞m=1m^αa^p m )^1/p(Σ^∞n=1n^βb^qn )^1/qto hold? Under what conditions is the constant factor best when Hilbert’s type series inequality is established? What is the expression of the best constant factor? The study of these problems is undoubtedly of great significance. In this paper, using the techniques of real analysis and the method of weight function, the authors study and analyze the formal structure and parameter relation of Hilbert’s type series inequality with a homogeneous kernel, and obtain the necessary and sufficient condition for it to hold and the expression of its best constant factor. Finally, a discussion is presented of its applications in the operator theory.
作者
洪勇
曾志红
HONG Yong;ZENG Zhi-hong(Department of Mathematics,Guangdong Baiyun University,Guangzhou 510450,China;Editorial Department of Journal,Guangdong Second Normal University,Guangzhou 510303,China)
出处
《西南大学学报（自然科学版）》
CAS
CSCD
北大核心
2019年第12期61-68,共8页
Journal of Southwest University(Natural Science Edition)
基金
国家自然科学基金项目(61300204)
关键词
Hilbert型级数不等式
齐次核
充分必要条件
最佳常数因子
有界算子
Hilbert’s type series inequality
homogeneous kernel
necessary and sufficient condition
the best constant factor
bounded operator
