On the local solution of the tangential Cauchy-Riemann equations
type: Item
instance of: scholarly article
title: On the local solution of the tangential Cauchy-Riemann equations
zbMATH Open document ID: 0679.32019
DOI: 10.1016/S0294-1449(16)30321-3
author: Sidney M. Webster
published in: Annales de l'Institut Henri Poincaré. Analyse Non Linéaire
publication date: 1989-01-01T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/78173
review text: G. M. Khenkin has constructed explicit operators P and Q for the tangential Cauchy-Riemann complex on a suitably small domain D in a strictly pseudoconvex real hypersurface M in complex n-space. Under appropriate restrictions on D, Khenkin obtained the representation formula \[ \phi ={\bar \partial}_ bP\phi +Q {\bar \partial}_ b\phi \] for (0,s)-forms \(\phi\), \(1\leq s\leq n-3\), restricted to D. For \(U\subset \subset D\), the author derives a \(C^ k\)-norm estimate of the form \[ \| P\phi \|_{U,k}\leq K\| \phi \|_{D,k}. \] The same estimate holds for Q. Unfortunately, the constant K blows up as U increases to D. For the case \(k=0\), Khenkin has obtained such an estimate, where K remains bounded as U increases to D. Whether this is possible for \(K>0\) is open. The author applies his estimates elsewhere (see the following review) to the local CR embedding problem.
Mathematics Subject Classification ID: 32V40
zbMATH DE Number: 4112997
zbMATH Keywords: tangential Cauchy-Riemann complex
zbMATH Keywords: strictly pseudoconvex real hypersurface
MaRDI profile type: Publication
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OpenAlex ID: W2590940713
description: scientific article; zbMATH DE number 4112997