On extending $L^{2}$ holomorphic functions from complex hyperplanes
Abstract
The key to the proof of the Ohsawa-Takegoshi Extension Theorem is a certain -estimate. The purpose of this note is to show that the 'curvature term' that arises in the Kohn-Morrey-H\"{o}rmander inequality (or the Bochner-Kodaira technique) is sufficient to produce such an estimate. We exploit self boundedness of the gradients of the weight functions to change the weight with respect to which the adjoint is taken. The weights, on the other hand, are the usual ones used in this context.
Cite
@article{arxiv.1104.4305,
title = {On extending $L^{2}$ holomorphic functions from complex hyperplanes},
author = {Emil J. Straube and Giuseppe Zampieri},
journal= {arXiv preprint arXiv:1104.4305},
year = {2011}
}
Comments
This paper has been withdrawn by the authors due to an error in estimate (5). Correcting the estimate leads to a fractional exponent in the denominator of the left hand side of (1) in Theorem 1, and an additional log factor on the right hand side. As a result, the factor $\delta$ in the right hand side of (3) becomes $\log(\delta)\delta$. This just misses what is needed for a proof of the Ohsawa-Takegoshi Theorem. Since such a proof was the whole point of the note, the authors decided to withdraw it