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ON THE OPTIMAL EXTENSION THEOREM AND A QUESTION OF OHSAWA
Nagoya Mathematical Journal ( IF 0.8 ) Pub Date : 2020-10-23 , DOI: 10.1017/nmj.2020.34
SHA YAO 1 , ZHI LI 2 , XIANGYU ZHOU 3
Affiliation  

In this paper, we present a version of Guan-Zhou’s optimal $L^{2}$ extension theorem and its application. As a main application, we show that under a natural condition, the question posed by Ohsawa in his series paper VIII on the extension of $L^{2}$ holomorphic functions holds. We also give an explicit counterexample which shows that the question fails in general.



中文翻译:

关于最优扩展定理和大泽的一个问题

在本文中,我们提出了一个版本的 Guan-Zhou 最优 $L^{2}$ 扩展定理及其应用。作为一个主要应用,我们展示了在自然条件下,Ohsawa 在他的系列论文 VIII 关于 $L^{2}$ 全纯函数的扩展提出的问题是成立的。我们还给出了一个明确的反例,表明这个问题通常是失败的。

更新日期:2020-10-23
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