齐次核的半离散Hilbert型不等式取最佳常数因子的条件及应用  

Condition for half-discrete hilbert-type inequality with homogeneous kernel to take the best constant factor and its applications

作　　者：洪勇 曾志红[2] HONG Yong;ZENG Zhihong(Guangdong Baiyun College,Guangdong Guangzhou 510450,China;Guangdong University of Education,Guangdong Guangzhou 510303,China)

机构地区：[1]广东白云学院,广东广州510450 [2]广东第二师范学院,广东广州510303

出　　处：《南昌大学学报（理科版）》2019年第3期216-220,共5页Journal of Nanchang University(Natural Science)

基　　金：国家自然科学基金资助项目(61300204)

摘　　要：利用实分析技巧和权系数方法,讨论了具有齐次核的半离散Hilbert型不等式∫0^+∞∑n=1^∞K(n,x)anf(x)dx≤M‖a~‖p,α‖f‖q,β及取最佳常数因子的条件,最后讨论其在算子理论中的应用。By using the method of weight function and the technique of real analysis,a half-discrete Hilbert-type inequality with homogeneous kernel ∫0^+∞∑n=1^∞ K(n,x)anf(x) dx≤M‖a ~‖ p,α‖f‖ q,β andconditions to achieve the beat constant factor are discussed,and their applications in operator theory are considered.

关 键 词：齐次核 半离散Hilbert型不等式 最佳常数因子 有界算子 算子范数 

分 类 号：O178[理学—数学]