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ON THE OPTIMAL $L^{2}$ EXTENSION THEOREM AND A QUESTION OF OHSAWA

Part of: Analytic continuation Differential operators in several variables Genetics and population dynamics Pluripotential theory Holomorphic convexity

Published online by Cambridge University Press:  23 October 2020

SHA YAO ,
ZHI LI  and
XIANGYU ZHOU
SHA YAO
Affiliation:
School of Mathematics and Information Science, Henan Polytechnic University, Henan454000, Chinayaosha@hpu.edu.cn
ZHI LI*
Affiliation:
School of Mathematical Sciences, Peking University, Beijing100871, China
XIANGYU ZHOU*
Affiliation:
Department of Mathematics, Shanghai University, Shanghai200444, China Institute of Mathematics, AMSS, Chinese Academy of Sciences, Beijing 100190, China
*
*Corresponding authors lizhi@amss.ac.cnxyzhou@math.ac.cn
*Corresponding authors lizhi@amss.ac.cnxyzhou@math.ac.cn
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Abstract

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.

MSC classification

Primary: 32D15: Continuation of analytic objects
Secondary: 32E10: Stein spaces, Stein manifolds 32W05: $overlinepartial$ and $overlinepartial$-Neumann operators 32U05: Plurisubharmonic functions and generalizations
Type
Article
Information
Nagoya Mathematical Journal , Volume 245 , March 2022 , pp. 154 - 165
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Copyright
© (2020) The Authors. The publishing rights in this article are licenced to Foundation Nagoya Mathematical Journal under an exclusive license

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