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The hyper-singular cousin of the Bergman projection


Authors: Guozheng Cheng, Xiang Fang, Zipeng Wang and Jiayang Yu
Journal: Trans. Amer. Math. Soc.
MSC (2010): Primary 47B34, 47G10
DOI: https://doi.org/10.1090/tran/6923
Published electronically: May 30, 2017
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Abstract: The Bergman projection over the unit disk is one of the most studied objects in complex analysis and operator theory. In this paper the new finding is to observe some unexpected patterns in boundedness when we consider the hyper-singular cousins of the Bergman projection. We also show that these patterns don't hold for the half-space, but we conjecture that they hold for general bounded domains.


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Additional Information

Guozheng Cheng
Affiliation: School of Mathematics, Wenzhou University, Wenzhou 325035, People’s Republic of China
Email: gzhcheng@wzu.edu.cn

Xiang Fang
Affiliation: Department of Mathematics, National Central University, Chung-Li 32001, Taiwan
Email: xfang@math.ncu.edu.tw

Zipeng Wang
Affiliation: College of Mathematics and Information Sciences, Shaanxi Normal University, Xi’an 710062, People’s Republic of China – and – Department of Mathematics, National Central University, Chung-Li 32001, Taiwan
Email: zipengwang11@fudan.edu.cn

Jiayang Yu
Affiliation: School of Mathematics, Sichuan University, Chengdu 610064, People’s Republic of China
Email: jiayangyu@scu.edu.cn

DOI: https://doi.org/10.1090/tran/6923
Keywords: Bergman projection, integral operator, unit disk, reproducing kernel
Received by editor(s): June 9, 2015
Received by editor(s) in revised form: December 9, 2015, and February 12, 2016
Published electronically: May 30, 2017
Additional Notes: The first author was supported by NSFC (11471249) and Zhejiang Provincial NSFC (LY14A010021)
The second author was supported by NSC of Taiwan (102-2115-M-008-016-MY2)
The third author was supported by NSFC (11371096).
The fourth author was supported by NSFC (11271075).
Article copyright: © Copyright 2017 American Mathematical Society