从齐次核向非齐次核发展的Hilbert型积分不等式的研究进展

Progress in the Study of Hilbert-Type Integral Inequalities from Homogeneous Kernels to Non-Homogeneous Kernels

Hilbert型积分不等式理论由于在积分算子的有界性及算子范数的研究中具有重要意义,因此近年来得到了较快发展.从最初对齐次核情形的讨论逐步向非齐次核情形扩展,已形成较为完整的理论体系.对这一发展过程及目前的研究现状进行综述,系统地展现Hilbert型积分不等式理论从齐次核向非齐次核发展的研究脉络.

Hilbert-type integral inequality theory,due to its significance in the study of boundedness and operator norm of integral operator,it has been developed more rapidly in recent years.Gradually expanding from the initial discussion of homogeneous case to non-homogeneous case,a more complete theoretical system has been formed.This paper provides an overview of this development process and the current state of research,systematically demonstrates the development of Hilbert-type integral inequalities from homogeneous kernels to nonhomogeneous kernels.