Arkiv för Matematik

Volume 60 (2022)

Number 2

On Hedenmalm–Shimorin type inequalities

Pages: 351 – 364



Yong Han (College of Mathematics and Statistics, Shenzhen University, Shenzhen, Guangdong, China)

Yanqi Qiu (School of Mathematics and Statistics, Wuhan University, Wuhan, Hubei, China; and Institute of Mathematics, AMSS, Chinese Academy of Sciences, Beijing, China)

Zipeng Wang (College of Mathematics and Statistics, Chongqing University, Chongqing, China)


We present a direct proof of an Hedenmalm–Shimorin inequality for short antidiagonals proved recently in [HS20, Advances in Mathematics, 2020] and give the three tensor analogue of such inequality.


Gaussian analytic functions, contractive operators, weighted Bergman spaces

2010 Mathematics Subject Classification

Primary 30B20. Secondary 15A45, 15A60.

Y. Qiu is supported by grants NSFC Y7116335K1, NSFC 11801547, and NSFC 11688101 of the National Natural Science Foundation of China. Z. Wang is supported by NSFC 11601296.

Received 14 September 2021

Received revised 28 November 2021

Accepted 30 May 2022

Published 26 October 2022