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

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.

arXiv commentAccepted for publication in Analysis & PDE