Coanalytic models for Hardy-type operators  

作　　者：Xiangdi Fu Kunyu Guo Fugang Yan 

机构地区：[1]School of Mathematical Sciences,Fudan University,Shanghai 200433,China

出　　处：《Science China Mathematics》2024年第12期2771-2788,共18页中国科学（数学英文版）

基　　金：supported by the National Natural Science Foundation of China(Grant No.12231005);the Shanghai Science and Technology Innovation Action Plan(Grant No.21ZR1404200);supported by the China Postdoctoral Science Foundation(Grant Nos.2020TQ0077 and 2020M681134)。

摘　　要：We establish coanalytic models for a broad class of Hardy-type operators on L^(2)[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 L_(p)[0,1]and obtain results concerning their boundedness,operator norms,and spectra.

关 键 词：Hardy operator Hardy inequality coanalytic model Bergman space 

分 类 号：O177[理学—数学]