English

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 Cn\mathbb{C}^{n}. 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