一类非齐次核有界积分算子的反问题  

Inverse Problem for a Class of Bounded IntegralOperators with Non-homogeneous Kernel

作　　者：张丽娟 洪勇 廖建全[2] ZHANG Lijuan;HONG Yong;LIAO Jianquan(College of Data Science,Guangzhou Huashang College,Guangzhou 511300,China;College of Mathematics,Guangdong University of Education,Guangzhou 510303,China)

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

出　　处：《吉林大学学报（理学版）》2024年第4期858-865,共8页Journal of Jilin University:Science Edition

基　　金：广东省基础与应用基础研究基金(批准号:2022A1515012429);广东省重点建设学科科研能力提升项目(批准号:2021ZDJS056);广州华商学院导师制项目(批准号:2022HSDS04)。

摘　　要：基于有界算子的本质之一:当原象集有界时象集一定有界,提出算子有界的反问题,即当算子T的象集有界时,如何判断其原象集有界.先引入算子反向有界的概念,再利用权函数方法和实分析技巧,讨论积分算子反向有界的等价参数条件,并给出反向有界积分算子的构造定理.最后给出一些特例.One of the essence of bounded operators is that the image set must be bounded when the original image set is bounded,we propose the inverse problem of operator boundedness:how to determine the boundedness of the original image set of an operator T when its image set is bounded.We first introduce the concept of operator reverse boundedness,and then use weight function method and real analysis techniques to discuss the equivalent parametric conditions for reverse boundedness of integral operators,and give a construction theorem for reverse boundedness of integral operators.Finally,some special cases are given.

关 键 词：非齐次核 积分算子 反向有界算子 逆向Hilbert型积分不等式 构造定理 

分 类 号：O178[理学—数学]