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.
Hardy operatorHardy inequalitycoanalytic modelBergman space
Xiangdi Fu、Kunyu Guo、Fugang Yan
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School of Mathematical Sciences,Fudan University,Shanghai 200433,China
College of Mathematics and Statistics,Chongqing University,Chongqing 401331,China
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