The Bergman projection in $L^p$ for domains with minimal smoothness

Loredana Lanzani; Elias M. Stein

The Bergman projection in $L^p$ for domains with minimal smoothness

Complex Variables 2012-10-08 v2 Analysis of PDEs Classical Analysis and ODEs Functional Analysis

Authors: Loredana Lanzani , Elias M. Stein

Abstract

Let $D\subset\mathbb C^n$ be a bounded, strongly Levi-pseudoconvex domain with minimally smooth boundary. We prove $L^p(D)$ -regularity for the Bergman projection $B$ , and for the operator $|B|$ whose kernel is the absolute value of the Bergman kernel with $p$ in the range $(1,+\infty)$ . As an application, we show that the space of holomorphic functions in a neighborhood of $\bar{D}$ is dense in $\vartheta L^p (D)$ .

Keywords

Bergman projection Levi-pseudoconvex domain minimal smoothness $L^p$-regularity Bergman kernel holomorphic functions

Cite

@article{arxiv.1201.4148,
  title  = {The Bergman projection in $L^p$ for domains with minimal smoothness},
  author = {Loredana Lanzani and Elias M. Stein},
  journal= {arXiv preprint arXiv:1201.4148},
  year   = {2012}
}

Related papers

View all related →