Sup-norm estimates for \({\bar\partial}\) in \({\mathbb{C}}^ 2\)
type: Item
instance of: scholarly article
title: Sup-norm estimates for \({\bar\partial}\) in \({\mathbb{C}}^ 2\)
zbMATH Open document ID: 0589.32038
DOI: 10.2307/1971275
published in: Annals of Mathematics. Second Series
publication date: 1986-01-01T00:00:00Z
review text: This is the first really deep result about uniform estimates for the \({\bar \partial}\)-problem in fifteen years. While the overall method - that of constructing an integral formula using the Henkin method - is not new, the specific method for constructing the function \(\Phi\) (z,\(\xi)\) needed for the Cauchy-Fantappié formalism is very new and is important. In particular, unlike previous constructions, \(\Phi\) (z,\(\xi)\) is constructed microlocally; such a delicate construction is necessary because the domains in question do not necessarily have local holomorphic separating functions. The paper relies on earlier deep work of Bedford and the author about peak functions on finite type domains in \({\mathbb{C}}^ 2\). Both that and the present one are delicate and are hard work to read. But they should prove to be valuable tools in future analysis.
Mathematics Subject Classification ID: 32W05
Mathematics Subject Classification ID: 35N15
Mathematics Subject Classification ID: 32A25
Mathematics Subject Classification ID: 32T99
zbMATH DE Number: 3946612
zbMATH Keywords: Cauchy-Riemann equations
zbMATH Keywords: uniform estimates for the \({\bar \partial }\)- problem
zbMATH Keywords: integral formula
author: J. E. Fornæss
reviewed by: Steven G. Krantz
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2307/1971275
OpenAlex ID: W2333862983
description: scientific article; zbMATH DE number 3946612