Extension of L^2 holomorphic functions

TL;DR

This paper simplifies the proof of the Ohsawa-Takegoshi Extension Theorem by showing that the necessary di-bar-estimate follows directly from the Hormander-Kohn-Morrey weighted inequality, avoiding complex arguments.

Contribution

It demonstrates that the di-bar-estimate can be derived from the weighted inequality without the Donnelly-Fefferman argument, streamlining the proof of the extension theorem.

Findings

Di-bar-estimate is a consequence of Hormander-Kohn-Morrey inequality

Simplifies the proof of Ohsawa-Takegoshi Extension Theorem

Uses a single non-singular weight family

Abstract

The purpose of this note is to show that the di-bar-estimate which is needed in the Ohsawa-Takegoshi Extension Theorem [6] is a direct consequence of the Hormander-Kohn-Morrey weigthed inequality. In this inequality, the Donnelly-Fefferman argument is not required and a single 1-parameter family of non-singular weights is used. This paper is the furtherst step of a great deal of work devoted to the simplification of the original proof of Ohsawa-Takegoshi Theorem, among other papers on the subject, we mention [1] and [8] which are based on "twisted" basic estimates and, in recent time, [3] and [9].