Cauchy-Riemann equation in real ellipsoids of \(\mathbb{C}^n\)
type: Item
instance of: scholarly article
title: Cauchy-Riemann equation in real ellipsoids of \(\mathbb{C}^n\)
zbMATH Open document ID: 0930.32006
author: Emmanuel Mazzilli
published in: Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI
publication date: 2000-02-09T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/73464
review text: The author solves the \(\overline\partial\)-equation with optimal \(L^p\) estimates in real ellipsoids of \(\mathbb{C}^n\). The main tools are the weighted integral formulas of \textit{B. Berndtsson} and \textit{M. Andersson} [Ann. Inst. Fourier 32, No. 3, 91-110 (1982; Zbl 0498.32001)] as well as the special support function constructed by \textit{K. Diederich}, \textit{J. E. Fornaess} and \textit{J. Wiegerinck} [Manuscr. Math. 56, 399-417 (1986; Zbl 0602.32006)]. The proof is based on elementary, but subtle, estimates of the corresponding integral kernels.
reviewed by: Vincent Thilliez
Mathematics Subject Classification ID: 32A25
Mathematics Subject Classification ID: 32W05
Mathematics Subject Classification ID: 32A07
zbMATH DE Number: 1279202
zbMATH Keywords: \(\overline\partial\)-operator
zbMATH Keywords: real ellipsoids in \(\mathbb{C}^n\)
zbMATH Keywords: integral formulas
MaRDI profile type: Publication
OpenAlex ID: W2330163920
cites work: Henkin-Ramirez kernels with weight factors
cites work: Optimal \(L^ p\) estimates for the \(\bar \partial\)-equation on complex ellipsoids in \(\mathbb{C}^ n\)
cites work: Sharp Hölder estimates for \({\bar\partial}\) on ellipsoids
cites work: INTEGRAL REPRESENTATION OF FUNCTIONS IN STRICTLY PSEUDOCONVEX DOMAINS AND APPLICATIONS TO THE $ \overline{\partial}$-PROBLEM
cites work: Optimal Lipschitz and \(L^p\) regularity for the equation \(\overline\partial u=f\) on strongly pseudo-convex domains
cites work: Q3992196
DOI: 10.5802/AFST.909
description: scientific article; zbMATH DE number 1279202