Distributional boundary values of holomorphic functions on product domains

TL;DR

This paper establishes that holomorphic functions with polynomial growth on domains with corners possess distributional boundary values when corners are generic CR manifolds, extending classical theorems to product domains.

Contribution

It introduces a framework for distributional boundary values of holomorphic functions on domains with corners, generalizing the Bochner-Hartogs theorem to product domains.

Findings

Holomorphic functions on domains with corners have distributional boundary values.

An analog of the Bochner-Hartogs theorem is proved for these boundary values.

Results apply to product domains with corners modeled as CR manifolds.

Abstract

We show that holomorphic functions of polynomial growth on domains with corners have distributional boundary values in an appropriate sense, provided the corners are generic CR manifolds. We prove an analog of the Bochner-Hartogs theorem for these boundary values for the simplest such domains, the product domains.