拟齐次核的Hilbert型积分不等式的适配参数条件  

The Adaptation Parameter Conditions for Hilbert-type Integral Inequalities with Quasi-homogeneous Kernels

作　　者：曾志红 洪勇 张然然[3] 田德路 ZENG Zhihong;HONG Yong;ZHANG Ranran;TIAN Delu(Editorial Department of Journal, Guangdong University of Education, Guangzhou 510303, China;Department of Applied Mathematics, Guangzhou Huashang College, Guangzhou 511300, China;School of Mathematics, Guangdong University of Education, Guangzhou 510303, China)

机构地区：[1]广东第二师范学院学报编辑部,广州510303 [2]广州华商学院应用数学系,广州511300 [3]广东第二师范学院数学学院,广州510303

出　　处：《华南师范大学学报（自然科学版）》2021年第5期108-112,共5页Journal of South China Normal University(Natural Science Edition)

基　　金：国家自然科学基金项目(11801092);广东省普通高校特色创新类项目(2019KTSCX119);广州市科技计划项目(201804010088)。

摘　　要：利用权系数方法和实分析技巧,讨论如何选取适配参数而获得具有最佳常数因子的拟齐次Hilbert型积分不等式,得到构建最佳拟齐次Hilbert型积分不等式的适配参数的充分必要条件,并得到最佳常数因子的表达式,从而解决了构建最佳Hilbert型积分不等式研究中的一个基本理论问题;最后讨论所得结论在求积分算子范数中的应用.The weighting coefficient method and real analysis techniques are used to discuss how to select the adaptation parameters to obtain Hilbert-type integral inequalities with quasi-homogeneous kernel and the best constant factor.The necessary and sufficient conditions for the adaptation parameters for constructing the best Hilbert-type integral inequality with quasi-homogeneous kernel and the expression formula of the best constant factor are obtained.This solves a fundamental theoretical problem in the study of constructing optimal Hilbert-type integral inequalities.Finally,its applications to finding the norm of integration operators are discussed.

关 键 词：HILBERT型积分不等式 最佳常数因子 适配参数 充分必要条件 算子范数 拟齐次核 

分 类 号：O178[理学—数学]