On smoothing properties of the Bergman projection
Complex Variables
2019-12-30 v2
Abstract
We study smoothing properties of the Bergman projection and also of weighted Bergman projections. In particular, we relate these properties to the hyperconvexity index of a pseudoconvex domain in . The notion of a hyperconvexity index was first introduced by B.Y. Chen, which provides a flexible criterion for studying geometric properties of hyperconvex domains. We also obtain a new estimate of weighted Bergman projections, which improves a well-known estimate of Berndtsson and Charpentier. We give several applications of this estimate, including the study of smoothing properties of weighted Bergman projections.
Keywords
Cite
@article{arxiv.1912.03473,
title = {On smoothing properties of the Bergman projection},
author = {Phung Trong Thuc},
journal= {arXiv preprint arXiv:1912.03473},
year = {2019}
}
Comments
Some additions and corrections are added, for instance in Theorem 1.3 and Theorem 1.4