Hardy空间上的Volterra-复合算子  

Volterra-Composition Operator on the Hardy Spaces

作　　者：丁宣浩[1,2] 邵长慧 李永宁 DING Xuanhao;SHAO Changhui;LI Yongning(School of Mathematics and Statistics,Chongqing Technology and Business University,Chongqing 400067,China;Chongqing Key Laboratory of Social Economy and Applied Statistics,Chongqing 400067,China)

机构地区：[1]重庆工商大学数学与统计学院,重庆400067 [2]经济社会应用统计重庆市重点实验室,重庆400067

出　　处：《西南师范大学学报（自然科学版）》2023年第2期40-45,共6页Journal of Southwest China Normal University(Natural Science Edition)

基　　金：国家自然科学基金项目(11871122,12101092);重庆市自然科学基金项目(CSTB2022NSCQ-MSX1045,cstc2020jcyj-msxmX0318);重庆市教委基金项目(KJQN202100822).

摘　　要：Hardy空间是一类在单位圆盘上的很重要的解析函数空间,其上的Volterra算子经过广泛的研究,已经获得了很显著的理论成果.复合算子理论也建立起了算子理论研究与函数论中经典问题研究之间的桥梁.记H^(2)为单位圆盘D上的Hardy空间.通过对H^(2)上的Volterra算子V以及复合算子Cφ的研究,本文引入了Hardy空间上的Volterra-复合算子Vφ,给出了Vφ的有界性、紧性、核的刻画,同时还研究了Vφ的特征值及其奇异值.Hardy space is a kind of very important analytic function spaces on the unit disk.Volterra operators on Hardy space have been extensively studied and have been obtained very significant theoretical results.The theory of complex operators also establishes a bridge between the study of operator theory and the study of classical problems in function theory.Denote H^(2)the Hardy space on the unit disk D,in this paper,we introduce the Volterra-composition operators Vφon Hardy spaces of the unit disk by studying Volterra operators V and composition operators Cφin H^(2).We give characterizations of the boundedness,compactness and the kernel of Vφ,and we also study the eigenvalues and singular values of Vφ.

关 键 词：HARDY空间 Volterra-复合算子 有界性 紧性 核 特征值 奇异值 

分 类 号：O177.1[理学—数学]