The hyper-singular cousin of the Bergman projection

Cheng, Guozheng; Fang, Xiang; Wang, Zipeng; Yu, Jiayang

doi:10.1090/tran/6923

The hyper-singular cousin of the Bergman projection
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by Guozheng Cheng, Xiang Fang, Zipeng Wang and Jiayang Yu PDF

Trans. Amer. Math. Soc. 369 (2017), 8643-8662 Request permission

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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