BekolléBonami 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 BekolléBonami 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 eprints
 Pub Date:
 January 2020
 DOI:
 10.48550/arXiv.2001.07868
 arXiv:
 arXiv:2001.07868
 Bibcode:
 2020arXiv200107868H
 Keywords:

 Mathematics  Complex Variables;
 Mathematics  Classical Analysis and ODEs;
 32A25;
 32A36;
 32A50;
 42B20;
 42B35
 EPrint:
 28 pages. An application to the weaktype estimate is added as a new section