Skoda's $L^2$ division theorem for $L^2$-optimal pairs

TL;DR

This paper proves a new Skoda-type $L^2$ division theorem for $L^2$-optimal pairs, employing novel inequalities, and uses it to characterize domains of holomorphy.

Contribution

It introduces a new Skoda-type division theorem for $L^2$-optimal pairs using innovative inequalities, advancing the understanding of holomorphic domain characterizations.

Findings

Established a Skoda-type $L^2$ division theorem for $L^2$-optimal pairs

Derived a new Bochner-type inequality from $L^2$-optimal conditions

Provided new characterizations of domains of holomorphy

Abstract

We establish a Skoda-type $L^2$ division theorem for $L^2$-optimal pairs, using a technique that combines a new Bochner-type inequality derived from the $L^2$-optimal conditions and Skoda's basic inequality. As applications, we provide some new characterizations of domains of holomorphy.