吉林大学学报（理学版）2024，Vol.62Issue(4)：858-865,8.DOI:10.13413/j.cnki.jdxblxb.2023498
一类非齐次核有界积分算子的反问题
Inverse Problem for a Class of Bounded Integral Operators with Non-homogeneous Kernel
摘要
Abstract
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Key words
non-homogeneous kernel/integral operator/reverse bounded operator/inverse Hilbert-type integral inequality/construction theorem分类
数理科学引用本文复制引用
张丽娟,洪勇,廖建全..一类非齐次核有界积分算子的反问题[J].吉林大学学报（理学版）,2024,62(4):858-865,8.基金项目
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)和广州华商学院导师制项目(批准号:2022HSDS04). （批准号:2022A1515012429）
