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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Sampling measure on Bergman spaces
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by Zhengyuan Zhuo and Shanli Ye
Proc. Amer. Math. Soc. 151 (2023), 4817-4825
Published electronically: August 4, 2023


In this paper, we investigate the relationship between sampling measure $\mu$, Berezin transform $\tilde {\mu }$ and $r$-averaging transform $\widehat {\mu }_r$ on Bergman spaces. Compared with some results of Luecking [Amer. J. Math. 107 (1985), pp. 85–111], our results provide an equivalent description of sampling measures, which reveals the reason why $1/\hat {\mu }_r\in L^\infty$ or $1/\tilde {\mu }\in L^\infty$ does not make sure that $\mu$ is a sampling measure on Bergman spaces.
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Bibliographic Information
  • Zhengyuan Zhuo
  • Affiliation: School of Mathematics and Systems Science, Guangdong Polytechnic Normal University, Guangzhou, 510665, People’s Republic of China
  • MR Author ID: 1016151
  • Email:
  • Shanli Ye
  • Affiliation: School of Science, Zhejiang University of Science and Technology, Hangzhou, 310023, People’s Republic of China
  • ORCID: 0000-0002-5264-5738
  • Email:
  • Received by editor(s): January 13, 2023
  • Received by editor(s) in revised form: February 20, 2023, and April 14, 2023
  • Published electronically: August 4, 2023
  • Additional Notes: Research was supported by Guangdong Basic and Applied Basic Research Foundation (2020A1515110493), the Natural Science Research Project of Guangdong Education Department, China (2020KQNCX042), Guangdong Polytechnic Normal University Science Foundation(2021SDKYA154) and Zhejiang Provincial Natural Science Foundation of China(LY23A010003)
    The first author is the corresponding author
  • Communicated by: Javad Mashreghi
  • © Copyright 2023 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 151 (2023), 4817-4825
  • MSC (2020): Primary 30H20, 46G12
  • DOI:
  • MathSciNet review: 4634885