圆周上的小Hankel算子  

The Little Hankel Operator on the Unit Circle

作　　者：李永宁 梁焕超 丁宣浩[1,2] LI Yong-ning;LIANG Huan-chao;DING Xuan-hao(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：《西南大学学报（自然科学版）》2021年第6期89-94,共6页Journal of Southwest University(Natural Science Edition)

基　　金：国家自然科学基金项目(11871122);重庆市自然科学基金项目(cstc2018jcyjAX0595,cstc2020jcyj-msxmX0318);重庆工商大学基金项目(2053010).

摘　　要：设u为非常值的内函数,单位圆周上的小Hankel算子是从uH^(2)到zH^(2)的线性算子,可视为由经典的Hardy空间上的Hankel算子在uH^(2)上的限制得到的算子,但其性质与Hardy空间上的Hankel算子的性质仍有一定的差别.根据Hardy空间上经典的Hankel算子理论,完全刻画了uH^(2)上的小Hankel算子的有界性、有限秩性质以及两个小Hankel算子的乘积的有限秩性质.Let u be a nonconstant inner function.The little Hankel operator on the unit circle is a linear operator from uH^(2) to zH^(2),which can be viewed as the restriction of Hankel operator on the classical Hardy space to uH^(2),but some of its properties are quite different from those of the Hankel operator on Hardy space.In this paper,based on the classical Hankel operator theory on Hardy space,we completely characterize the boundedness and the finite rank property of the little Hankel operator and describe the finite rank property of the product of two little Hankel operators.

关 键 词：小Hankel算子 有界性 有限秩 HARDY空间 

分 类 号：O177[理学—数学]