The Chirka-Lindelöf and Fatou theorems for \(\overline{\partial}_J\)-subsolutions
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)].
scientific article; zbMATH DE number 7318490
scientific article