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$ L^p$ estimates for the Bergman projection on some Reinhardt domains


Author: Zhenghui Huo
Journal: Proc. Amer. Math. Soc. 146 (2018), 2541-2553
MSC (2010): Primary 32A25, 32A36, 32A07
DOI: https://doi.org/10.1090/proc/13932
Published electronically: January 26, 2018
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Abstract: We obtain $ L^p$ regularity for the Bergman projection on some Reinhardt domains. We start with a bounded initial domain $ \Omega $ with some symmetry properties and generate successor domains in higher dimensions. We prove: If the Bergman kernel on $ \Omega $ satisfies appropriate estimates, then the Bergman projection on the successor is $ L^p$ bounded. For example, the Bergman projection on successors of strictly pseudoconvex initial domains is bounded on $ L^p$ for $ 1<p<\infty $. The successor domains need not have smooth boundary nor be strictly pseudoconvex.


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Zhenghui Huo
Affiliation: Department of Mathematics, Washington University in St. Louis, 1 Brookings Drive, St. Louis, Missouri 63130
Email: huo@math.wustl.edu

DOI: https://doi.org/10.1090/proc/13932
Keywords: Bergman projection, Bergman kernel, $L^p$ boundedness, Reinhardt domain
Received by editor(s): March 15, 2017
Received by editor(s) in revised form: August 20, 2017, August 24, 2017, and August 25, 2017
Published electronically: January 26, 2018
Communicated by: Harold P. Boas
Article copyright: © Copyright 2018 American Mathematical Society

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