广义齐次核重积分算子最佳搭配参数的等价条件及应用  

Equivalence condition for the best matching parameters of multiple integral operator with generalized homogeneous kernel and applications

作　　者：洪勇 陈强[2] Yong Hong;Qiang Chen

机构地区：[1]广州华商学院数据科学学院,广州511300 [2]广东第二师范学院计算机学院,广州510303

出　　处：《中国科学：数学》2023年第5期717-728,共12页Scientia Sinica：Mathematica

基　　金：国家自然科学基金(批准号:61772140);广州华商学院科研团队项目(批准号:2021HSKT03);广东省基础与应用基础研究基金(批准号:2022A1515012429)资助项目。

摘　　要：引入搭配参数a1,a2,...,an并应用权函数方法,可得到重积分算子T:■的不等式■若常数因子M(a1,a2,...,an)等于T:■的算子范数||T||,则称a1,a2,...,an为算子T的最佳搭配参数.本文针对广义齐次核,讨论算子T的最佳搭配参数的充分必要条件,得到算子T有界的判定方法和算子范数计算公式.最后作为应用给出一些特例.By introducing the matching parameters a1,a2,...,an and using the weight function method,the inequality■can be obtained for the operator T:■If the constant factor M(a1,a2,...,an)is the operator norm||T||of T:■then a1,a2,...,an are called the best matching parameters of the operator T.In this paper,for the generalized homogeneous kernel,the necessary and sufficient conditions for the best matching parameters of the operator T are discussed,as the method of determining that the operator T is bounded and the calculation formula for the operator norm of T are obtained.Finally,some special cases are given as applications.

关 键 词：广义齐次核 重积分算子 有界算子 算子范数 HILBERT型不等式 最佳搭配参数 等价条件 

分 类 号：O177.6[理学—数学]