On an observation of Sibony

TL;DR

This paper proves that holomorphic functions on certain Reinhardt domains in complex space extend holomorphically near the origin if the boundary contains the origin, highlighting a boundary regularity property.

Contribution

It establishes a boundary extension property for holomorphic functions on Reinhardt domains with the origin on the boundary, a new result in complex analysis.

Findings

Holomorphic functions extend holomorphically near the origin

Boundary containing the origin implies extension property

Applicable to Reinhardt domains in complex space

Abstract

It is shown that if the boundary of a Reinhardt domain in $\mathbb{C}^n$ contains the origin, each holomorphic function on the domain which is infinitely many times differentiable up to the boundary extends holomorphically to a neighborhood of the origin.