指数权的加权Lebesgue空间中拟齐次核最优Hilbert型积分不等式的参数条件及应用  

Parameter Conditions of Optimal Hilbert-Type Integral Inequalitieswith Quasi-homogeneous Kernel in Weighted Lebesgue Spaceswith Exponential Weight and Applications

作　　者：赵茜 洪勇 孔荫莹 ZHAO Qian;HONG Yong;KONG Yinying(College of Artificial Intelligence,Guangzhou Huashang College,Guangzhou 511300,China;College of Statistics and Mathematics,Guangdong University of Finance and Ec onomics,Guangzhou 510320,China)

机构地区：[1]广州华商学院人工智能学院,广州511300 [2]广东财经大学统计与数学学院,广州510320

出　　处：《吉林大学学报（理学版）》2024年第6期1325-1333,共9页Journal of Jilin University:Science Edition

基　　金：广州华商学院导师制项目(批准号:2024HSDS10);广东省基础与应用基础研究基金(批准号:2022A1515012429).

摘　　要：首先,引入拟齐次核的概念,讨论权函数为指数函数的加权Lebesgue空间中具有拟齐次核的Hilbert型积分不等式;其次,利用权系数方法及若干分析技巧,给出最优Hilbert型积分不等式的等价参数条件,并获得了最佳常数因子的计算公式;最后,讨论其在算子理论中的应用.Firstly,the concept of quasi-homogeneous kernel was introduced to discuss Hilbert-type integral inequalities with quasi-homogeneous kernel in weighted Lebesgue spaces with exponential functions.Secondly,by using the weight coefficient method and several analysis techniques,equivalent parameter conditio n for optimal Hilbert-type integral inequalities was given,and the calculation formula for the best constant factor was obtained.Finally,its applications in operator theory were discussed.

关 键 词：加权Lebesgue空间 拟齐次核 HILBERT型积分不等式 最佳搭配参数 等价条件 有界算子 算子范数 

分 类 号：O178[理学—数学]