Uniform estimates for \(\bar \partial\) on the intersection of two strictly pseudoconvex \(\mathbb C^2\)-domains without transversality condition
type: Item
instance of: scholarly article
title: Uniform estimates for \(\bar \partial\) on the intersection of two strictly pseudoconvex \(\mathbb C^2\)-domains without transversality condition
zbMATH Open document ID: 0653.32018
DOI: 10.1007/BF01442493
author: Klaus Peters
published in: Mathematische Annalen
publication date: 1989-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/164561
review text: Integral operators are constructed for solving the inhomogeneous Cauchy-Riemann equation on arbitrary intersections of two smooth, strictly pseudoconvex domains and uniform estimates for these operators are proved. This means that we generalize a result of \textit{P. L. Polyakov} [Mat. Sb., N. Ser. 88(130), 238--255 (1972; Zbl 0276.32009)] and \textit{R. M. Range} and \textit{Y.-T. Siu} [Math. Ann. 206, 325--354 (1973; Zbl 0248.32015)] from 1972/73. They constructed integral operators for solving the Cauchy-Riemann equation with uniform estimates on finite intersections of smooth, strictly pseudoconvex domains. But they used the additional hypothesis that these domains intersect transversally. In the paper we answer the question, whether the hypothesis on transversality can be omitted, affirmatively.
Mathematics Subject Classification ID: 32W05
Mathematics Subject Classification ID: 32T99
zbMATH DE Number: 4065410
zbMATH Keywords: integral operators
zbMATH Keywords: inhomogeneous Cauchy-Riemann equation
zbMATH Keywords: uniform estimates
MaRDI profile type: Publication
cites work: Q5621558
cites work: Q5543303
cites work: Ein Divisionsproblem und Randintegraldarstellungen in der komplexen Analysis
OpenAlex ID: W2073853687
description: scientific article; zbMATH DE number 4065410