The Bergman kernel and projection on non-smooth worm domains

TL;DR

This paper derives a detailed asymptotic expansion of the Bergman kernel on non-smooth worm domains, revealing boundary behavior, failure of Condition R, and L^p mapping properties, advancing understanding of complex analysis in these domains.

Contribution

It provides the first precise asymptotic expansion of the Bergman kernel on non-smooth worm domains, highlighting new boundary phenomena and functional properties.

Findings

Asymptotic expansion of the Bergman kernel obtained

Failure of Condition R demonstrated in these domains

L^p mapping properties of the kernel analyzed

Abstract

This paper provides a precise asymptotic expansion for the Bergman kernel on the non-smooth worm domains of Christer Kiselman in complex 2-space. Applications are given to the failure of Condition R, to deviant boundary behavior of the kernel, and to L^p mapping properties of the kernel.