Coanalytic models for Hardy-type operators

被引：0
|
作者：
Fu, Xiangdi [1 ]
Guo, Kunyu [1 ]
Yan, Fugang [1 ,2 ]
机构：
[1] Fudan Univ, Sch Math Sci, Shanghai 200433, Peoples R China
[2] Chongqing Univ, Coll Math & Stat, Chongqing 401331, Peoples R China
来源：
SCIENCE CHINA-MATHEMATICS | 2024年
基金：
中国国家自然科学基金; 中国博士后科学基金;
关键词：
Hardy operator; Hardy inequality; coanalytic model; Bergman space; THEOREM;
D O I：
10.1007/s11425-023-2192-2
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We establish coanalytic models for a broad class of Hardy-type operators on L2[0, 1]. In particular, we show that the logarithmic Hardy operator is unitarily equivalent to the difference between the identity operator and the backward shift on a Bergman-type space. This result leads to several applications related to zero sets and invariant subspaces in weighted Bergman spaces. Additionally, we study logarithmic Hardy operators on Lp[0, 1] and obtain results concerning their boundedness, operator norms, and spectra.
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页数：18
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