Integral representation formulas for differential forms on complex manifolds and applications to the \({\bar \partial}\)-equation
type: Item
instance of: scholarly article
title: Integral representation formulas for differential forms on complex manifolds and applications to the \({\bar \partial}\)-equation
zbMATH Open document ID: 0702.32004
DOI: 10.1007/BF01790354
published in: Annali di Matematica Pura ed Applicata. Serie Quarta
publication date: 1989-01-01T00:00:00Z
review text: The author derives an explicit global integral formula of Koppelman- Leray-Nourget type for differential forms on generalized analytic polyhedra on complex manifolds. Using this formula, the author gives explicit solution operator to the \({\bar \partial}\)-equation on strictly pseudoconvex polyhedra and proves that this solution admits uniform estimates.
Mathematics Subject Classification ID: 32A25
Mathematics Subject Classification ID: 32W05
Mathematics Subject Classification ID: 35N15
Mathematics Subject Classification ID: 35C15
Mathematics Subject Classification ID: 35F15
zbMATH DE Number: 4150634
zbMATH Keywords: integral formula of Koppelman-Leray-Nourget type
zbMATH Keywords: differential forms
zbMATH Keywords: analytic polyhedra
zbMATH Keywords: \({\bar \partial }\)-equation
zbMATH Keywords: strictly pseudoconvex polyhedra
Wikidata QID: Q115393172
author: T. Hatziafratis
reviewed by: Rodolfo Salvi
MaRDI profile type: Publication
cites work: Integral representations of differential forms on Cauchy-Riemann manifolds and the theory of CR-functions
cites work: Q3322388
cites work: Q5621558
cites work: Integral representation formulas on analytic varieties
cites work: An explicit Koppelman type integral formula on analytic varieties
cites work: CONTINUATION OF BOUNDED HOLOMORPHIC FUNCTIONS FROM SUBMANIFOLDS IN GENERAL POSITION TO STRICTLY PSEUDOCONVEX DOMAINS
cites work: Global integral formulas for solving the $\bar ∂$-equation on Stein manifolds
cites work: Q3692032
cites work: Q3898751
cites work: Uniform Estimates for the ∂-Equation on Pseudoconvex Polyhedra on Stein Manifolds
cites work: Hölder and Lp estimates for solutions of ∂u = f in strongly pseudoconvex domains
cites work: The Szegö kernel in terms of Cauchy-Fantappie kernels
cites work: The Cauchy integral for differential forms
cites work: Optimal Lipschitz and \(L^p\) regularity for the equation \(\overline\partial u=f\) on strongly pseudo-convex domains
cites work: Q3924489
cites work: Le calcul différentiel et intégral sur une variété analytique complexe. (Problème de Cauchy. III.)
cites work: Problémes sur les formes différentielles et les courants
cites work: Integral Representation Formulas and $L^p$-Estimates for the $\bar{\partial}$-Equation.
cites work: Integral representation formulas on strictly pseudoconvex domains in Stein manifolds
cites work: Ein Divisionsproblem und Randintegraldarstellungen in der komplexen Analysis
cites work: Q3719028
cites work: Uniform estimates for the \(\bar\partial\)-equation on domains with piecewise smooth strictly pseudoconvex boundaries
cites work: Q3958740
cites work: An integral formula for holomorphic functions on strictly pseudoconvex hypersurfaces
full work available at URL: https://doi.org/10.1007/bf01790354
OpenAlex ID: W2021250136
description: scientific article; zbMATH DE number 4150634