ON THE OPTIMAL EXTENSION THEOREM AND A QUESTION OF OHSAWA

2020 ◽  
pp. 1-12
Author(s):  
SHA YAO ◽  
ZHI LI ◽  
XIANGYU ZHOU
Keyword(s):  
Natural Condition ◽  
Extension Theorem ◽  
Holomorphic Functions ◽  
Main Application ◽  
Optimal Extension

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.

scholarly journals Holomorphic extension of generalizations ofHpfunctions

1985 ◽  
Vol 8 (3) ◽  
pp. 417-424 ◽  
Author(s):  
Richard D. Carmichael
Keyword(s):  
Convex Hull ◽  
Extension Theorem ◽  
Holomorphic Functions ◽  
Holomorphic Extension ◽  
Finite Union ◽  
Convex Cones ◽  
Recent Analysis ◽  
Boundary Values ◽  
Connected Component ◽  
Open Convex

In recent analysis we have defined and studied holomorphic functions in tubes inℂnwhich generalize the HardyHpfunctions in tubes. In this paper we consider functionsf(z),z=x+iy, which are holomorphic in the tubeTC=ℝn+iC, whereCis the finite union of open convex conesCj,j=1,…,m, and which satisfy the norm growth of our new functions. We prove a holomorphic extension theorem in whichf(z),z ϵ TC, is shown to be extendable to a function which is holomorphic inT0(C)=ℝn+i0(C), where0(C)is the convex hull ofC, if the distributional boundary values in𝒮′off(z)from each connected componentTCjofTCare equal.

scholarly journals The Ohsawa-Takegoshi Extension Theorem on Some Unbounded Sets

2007 ◽  
Vol 188 ◽  
pp. 19-30 ◽  
Author(s):  
Żywomir Dinew
Keyword(s):  
Bergman Spaces ◽  
Extension Theorem ◽  
Holomorphic Functions ◽  
Pseudoconvex Domains

AbstractWe use a method of Berndtsson to obtain a simplification of Ohsawa’s result concerning extension of L2-holomorphic functions. We also study versions of the Ohsawa-Takegoshi theorem for some unbounded pseudoconvex domains, with an application to the theory of Bergman spaces. Using these methods we improve some constants, that arise in related inequalities.

scholarly journals On the extension of L2 holomorphic functions V-Effects of generalization

2001 ◽  
Vol 161 ◽  
pp. 1-21 ◽  
Author(s):  
Takeo Ohsawa
Keyword(s):  
Extension Theorem ◽  
Holomorphic Functions ◽  
Extension Theory ◽  
Holomorphic Bundle

A general extension theorem for L2 holomorphic bundle-valued top forms is formulated. Although its proof is based on a principle similar to Ohsawa-Takegoshi’s extension theorem, it explains previous L2 extendability results systematically and bridges extension theory and division theory.

scholarly journals An extension theorem for separately holomorphic functions with analytic singularities

2003 ◽  
Vol 80 ◽  
pp. 143-161 ◽  
Author(s):  
Marek Jarnicki ◽  
Peter Pflug
Keyword(s):  
Extension Theorem ◽  
Holomorphic Functions ◽  
Analytic Singularities

scholarly journals Application and simplified proof of a sharp L2 extension theorem

2015 ◽  
Vol 220 ◽  
pp. 81-89 ◽  
Author(s):  
Takeo Ohsawa
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Bergman Kernel ◽  
Extension Theorem ◽  
Holomorphic Functions ◽  
Stability Theorem ◽  
Alternate Proof

AbstractAs an application of a sharp L2 extension theorem for holomorphic functions in Guan and Zhou, a stability theorem for the boundary asymptotics of the Bergman kernel is proved. An alternate proof of the extension theorem is given, too. It is a simplified proof in the sense that it is free from ordinary differential equations.

scholarly journals Application and simplified proof of a sharp L2 extension theorem

2015 ◽  
Vol 220 ◽  
pp. 81-89 ◽  
Author(s):  
Takeo Ohsawa
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Bergman Kernel ◽  
Extension Theorem ◽  
Holomorphic Functions ◽  
Stability Theorem ◽  
Alternate Proof

AbstractAs an application of a sharpL2extension theorem for holomorphic functions in Guan and Zhou, a stability theorem for the boundary asymptotics of the Bergman kernel is proved. An alternate proof of the extension theorem is given, too. It is a simplified proof in the sense that it is free from ordinary differential equations.

scholarly journals Holomorphic extension of generalizations ofHpfunctions. II

1987 ◽  
Vol 10 (1) ◽  
pp. 1-8 ◽  
Author(s):  
Richard D. Carmichael
Keyword(s):  
Extension Theorem ◽  
Holomorphic Functions ◽  
Holomorphic Extension ◽  
Previous Article

In a previous article we have obtained a holomorphic extension theorem (edge of the wedge theorem) concerning holomorphic functions in tubes inℂnwhich generalize the HardyHpfunctions for the cases1<p≤2. In this paper we obtain a similar holomorphic extension theorem for the cases2<p<∞.

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