Irregularity of the Bergman projection on worm domains in C^n

TL;DR

This paper constructs higher-dimensional worm domains and demonstrates that the Bergman projection operators are unbounded on high-order Sobolev spaces for all p in [1,∞), highlighting irregularity in these complex domains.

Contribution

It introduces higher-dimensional worm domains and proves the unboundedness of the Bergman projection on Sobolev spaces, extending known irregularity results to higher dimensions.

Findings

Bergman projection is unbounded on high-order Sobolev spaces.

Higher-dimensional worm domains exhibit irregularity in complex analysis.

Unboundedness holds for all p in [1,∞).

Abstract

We construct higher-dimensional versions of the Diederich-Fornaess worm domains and show that the Bergman projection operators for these domains are not bounded on high-order $L^p$-Sobolev spaces for $1\leq p<\infty.$