核为G(n^(λ1)x^(λ2))(λ11λ2>0)的半离散Hilbert型不等式成立的等价参数条件及应用  

Equivalent Parameter Condition for the Establishment of Half-Discrete Hilbert-Type Inequality with Kernel G(n^(λ1)x^(λ2))(λ1λ2>0)and Applications

作　　者：洪勇 李真 陈强 HONG Yong;LI Zhen;CHEN Qiang(Department of Applied Mathematics,Guangzhou Huashang College,Guangzhou 511300,China;College of Statistics and Mathematics,Guangdong University of Finance and Economics,Guangzhou 510320,China;Department of Computer Science,Guangdong University of Education,Guangzhou 510303,China)

机构地区：[1]广州华商学院应用数学系,广州511300 [2]广东财经大学统计与数学学院,广州510320 [3]广东第二师范学院计算机科学系,广州510303

出　　处：《数学年刊（A辑）》2021年第3期279-288,共10页Chinese Annals of Mathematics

基　　金：国家自然科学基金(No.61772140)的资助.

摘　　要：利用权函数方法和实分析技巧,在λ1λ2>0的条件下,讨论具有非齐次核K(n,x)=G(n^(λ1)x^(λ2))的半离散Hilbert型不等式成立的等价参数条件及最佳常数因子问题,最后讨论其在算子理论中的应用.By using the way of weight function and techniques of real analysis,in the case of λ11λ2>0,equivalent parameter condition for the establishment of half-discrete Hilbert-type inequality with kernel G(n^(λ1)x^(λ2))is given,the best possible constant factor is obtained,and theirs applications in operator theory are discussed.

关 键 词：非齐次核 充要条件 半离散Hilbert型不等式 有界算子 算子范数 

分 类 号：O178[理学—数学]