On the sharp $L^2$-estimates of Skoda division theorem

TL;DR

This paper establishes a sharp $L^2$-division theorem in complex analysis, providing new characterizations of plurisubharmonic functions and connecting to Guan-Zhou's extension theorem with improved estimates.

Contribution

It introduces a sharp $L^2$-division theorem and links it to characterizations of plurisubharmonic functions and existing extension theorems, advancing the theoretical understanding.

Findings

Proved a sharp $L^2$-division theorem

Provided new characterizations of plurisubharmonic functions

Connected the division theorem to Guan-Zhou's extension estimate

Abstract

In this paper, we prove a Skoda type division theorem with sharp $L^2$-estimate. Furthermore, using this estimate, we provide new characterizations of plurisubharmonic functions. We also explain that the sharp $L^2$-division theorem leads the Guan-Zhou's sharp $L^2$-estimate for extension theorem.