拟齐次核的Hilbert型重积分不等式最佳搭配参数的等价条件及应用  

Equivalence Conditions of the Optimal Matching Parameters for Hilbert-Type Multiple Integral Inequality with Quasi-homogeneous Kernel and Applications

作　　者：洪勇 陈强[2] 李真 HONY Yong;CHEN Qiang;LI Zhen(Department of Applied Mathematics,Guangzhou Huashang College,Guangzhou 511300,China;College of Computer Science,Guangdong University of Education,Guangzhou 510303,China;College of Statistics and Mathematics,Guangdong University of Finance and Economics,Guangzhou 510320,China)

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

出　　处：《数学年刊（A辑）》2022年第2期191-200,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,讨论拟齐次核Hilbert型重积分不等式的最佳搭配参数,得到最佳搭配参数的若干等价条件及不等式最佳常数因子的表达公式.最后讨论其在奇异积分算子理论中的应用.By using the weight function method,the optimal matching parameter conditions for Hilbert-type multiple integral inequality with quasi-homogeneous kernel are discussed,several equivalence conditions for optimal matching are obtained,and the formula for the expression of the best constant factor of the inequality is obtained.Finally,their applications to the theory of singular integral operator are discussed.

关 键 词：拟齐次核 Hilbert型重积分不等式 最佳常数因子 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]