Open Access
July, 2019 On sharper estimates of Ohsawa–Takegoshi $L^2$-extension theorem
J. Math. Soc. Japan 71(3): 909-914 (July, 2019). DOI: 10.2969/jmsj/80018001


We present an $L^2$-extension theorem with an estimate depending on the weight functions for domains in $\mathbb{C}$. When the Hartogs domain defined by the weight function is strictly pseudoconvex, this estimate is strictly sharper than known optimal estimates. When the weight function is radial, we prove that our estimate provides the $L^2$-minimum extension.

Funding Statement

The author is supported by Program for Leading Graduate Schools, MEXT, Japan. He is also supported by the Grant-in-Aid for Scientific Research (KAKENHI No.15J08115).


Download Citation

Genki HOSONO. "On sharper estimates of Ohsawa–Takegoshi $L^2$-extension theorem." J. Math. Soc. Japan 71 (3) 909 - 914, July, 2019.


Received: 5 March 2018; Published: July, 2019
First available in Project Euclid: 12 March 2019

zbMATH: 07121558
MathSciNet: MR3984247
Digital Object Identifier: 10.2969/jmsj/80018001

Primary: 32A07 , 32A10‎

Keywords: complex Monge–Ampère equation , Ohsawa–Takegoshi $L^2$ extension theorem , optimal estimate

Rights: Copyright © 2019 Mathematical Society of Japan

Vol.71 • No. 3 • July, 2019
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