Bekollé-Bonami estimates on some pseudoconvex domains
Abstract
We establish a weighted $L^p$ norm estimate for the Bergman projection for a class of pseudoconvex domains. We obtain an upper bound for the weighted $L^p$ norm when the domain is, for example, a bounded smooth strictly pseudoconvex domain, a pseudoconvex domain of finite type in $\mathbb C^2$, a convex domain of finite type in $\mathbb C^n$, or a decoupled domain of finite type in $\mathbb C^n$. The upper bound is related to the Bekollé-Bonami constant and is sharp. When the domain is smooth, bounded, and strictly pseudoconvex, we also obtain a lower bound for the weighted norm.
- Publication:
-
arXiv e-prints
- Pub Date:
- January 2020
- DOI:
- 10.48550/arXiv.2001.07868
- arXiv:
- arXiv:2001.07868
- Bibcode:
- 2020arXiv200107868H
- Keywords:
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- Mathematics - Complex Variables;
- Mathematics - Classical Analysis and ODEs;
- 32A25;
- 32A36;
- 32A50;
- 42B20;
- 42B35
- E-Print:
- 28 pages. An application to the weak-type estimate is added as a new section