加权Lebesgue空间中超齐次核有界积分算子的构造条件及范数计算公式  

Construction conditions for the bounded integral operator with the super-homogeneous kernel in the weighted Lebesgue space and the formula of the operator norm

作　　者：洪勇 Yong Hong

机构地区：[1]广州华商学院数据科学学院,广州511300 [2]广东财经大学统计与数学学院,广州510320

出　　处：《中国科学:数学》2025年第4期791-802,共12页Scientia Sinica:Mathematica

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

摘　　要：本文引入超齐次函数的概念,用超齐次核统一齐次核、广义齐次核及若干非齐次核.首先利用权函数方法讨论具有超齐次核的Hilbert型积分不等式;然后根据Hilbert型积分不等式与同核积分算子的联系,讨论具有超齐次核的积分算子,得到在加权Lebesgue空间中构造超齐次核有界积分算子的充分必要条件及算子范数的计算公式.In this paper,we introduce the concept of the super-homogeneous function,and use the superhomogeneous kernel to unify the homogeneous kernel,the generalized homogeneous kernel,and several nonhomogeneous kernels.We first discuss the Hilbert-type integral inequality with the super-homogeneous kernel by using the weight function method and real analysis technique,and then study the integral operator with the superhomogeneous kernel according to the relationship between the Hilbert-type integral inequality and the integral operator with the same kernel.Finally,we obtain the construction conditions of the bounded integral operator with the super-homogeneous kernel in the weighted Lebesgue space as well as the formula for the operator norm.

关 键 词：超齐次核 有界积分算子 HILBERT型积分不等式 加权Lebesgue空间 算子范数 构造条件 

分 类 号：O174.2[理学—数学]