$L^p$ estimates for the Bergman projection on some Reinhardt domains
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- by Zhenghui Huo PDF
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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.References
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Additional Information
- Zhenghui Huo
- Affiliation: Department of Mathematics, Washington University in St. Louis, 1 Brookings Drive, St. Louis, Missouri 63130
- MR Author ID: 1198280
- Email: huo@math.wustl.edu
- 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
- © Copyright 2018 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 146 (2018), 2541-2553
- MSC (2010): Primary 32A25, 32A36, 32A07
- DOI: https://doi.org/10.1090/proc/13932
- MathSciNet review: 3778156