The Chirka-Lindelöf and Fatou theorems for \(\overline{\partial}_J\)-subsolutions
type: Item
instance of: scholarly article
title: The Chirka-Lindelöf and Fatou theorems for \(\overline{\partial}_J\)-subsolutions
zbMATH Open document ID: 1470.32082
published in: Revista Matemática Iberoamericana
publication date: 2021-03-07T00:00:00Z
review text: The main purpose of this paper is to develop a function theory on almost complex manifolds. The key assumption is to impose suitable conditions on the \(\bar{\partial}_J\)-part of the differential of the functions under consideration. The goal of this paper is the study of boundary problems. Precisely, Chirka-Lindelöf and Fatou-type theorems for bounded \(C^1\) functions \(f\), with bounded \(\bar{\partial}_Jf\), on a strictly pseudoconvex domain in an almost complex manifold \((M,J)\), are proven. The results can be considered as generalization of works and methods of \textit{E. M. Stein} [Boundary behavior of holomorphic functions of several complex variables. Princeton, NJ: Princeton University Press (1972; Zbl 0242.32005)], \textit{E. M. Cirka} [Math. USSR, Sb. 21, 619--639 (1975; Zbl 0297.32001)] and \textit{A. Sadullaev} [Mat. Sb., Nov. Ser. 101(143), 568--583 (1976; Zbl 0346.32024)].
reviewed by: Antonella Nannicini
Mathematics Subject Classification ID: 32Q60
Mathematics Subject Classification ID: 53C15
zbMATH DE Number: 7318490
zbMATH Keywords: almost complex manifold
zbMATH Keywords: \( \overline{\partial}\)-operator
zbMATH Keywords: strictly pseudoconvex domain
zbMATH Keywords: Fatou's theorem
author: Alexandre Sukhov
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.4171/rmi/1172
OpenAlex ID: W2999261676
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DOI: 10.4171/RMI/1172
description: scientific article; zbMATH DE number 7318490