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 / 67卷 / 12期

基金：

中国博士后科学基金; 中国国家自然科学基金;

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.

引用

页码：2771 / 2788

页数：18

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