‎In this paper we investigate a two classes of domains in $mathbb{C}^n$ generalizing the Hartogs triangle‎. ‎We prove optimal estimates for the mapping properties of the Bergman projection on these domains.

Abstract We extend the Polydisk Theorem for symmetric bounded domains to Cartan–Hartogs domains, and apply it prove that a domain inherits totally geodesic submanifolds from which is based on, give characterization of Cartan–Hartogs’s geodesics with linear support.

Let X be a connected normal Stein space of pure dimension d ≥ 2 with isolated singularities only. By solving a weighted ∂-equation with compact support on a desingularization of X , we derive Hartogs’ Extension Theorem on X by the ∂-idea due to Ehrenpreis.

We prove an analog of the classical Hartogs extension theorem for CR L2 functions defined on boundaries of certain (possibly unbounded) domains on coverings of strongly pseudoconvex manifolds. Our result is related to a question formulated in the paper of Gromov, Henkin and Shubin [GHS] on holomorphic L2 functions on coverings of pseudoconvex manifolds.

Let X be a connected normal complex space of dimension n ≥ 2 which is (n − 1)-complete, and let π : M → X be a resolution of singularities. By use of Takegoshi’s generalization of the Grauert-Riemenschneider vanishing theorem, we deduce H cpt(M,O) = 0, which in turn implies Hartogs’ extension theorem on X by the ∂-technique of Ehrenpreis.

We study discrete analogues of holomorphic functions of one and two variables, especially those that were called monodiffric functions of the first kind by Rufus Isaacs. Discrete analogues of the Cauchy–Riemann operators, domains of holomorphy in one discrete variable, and the Hartogs phenomenon in two discrete variables are investigated.

The paper is devoted to the problem of R-analytic continuation functions several real variables which admit along parallel sections. We prove an analogue well-known Hartogs lemma for

Motivated by a result and a question by E. M. Chirka we consider the Hartogs’ extension property for some connected sets in C2 of the form K = Σ ∪ (∂Δ × Δ), where Σ is a possibly nonconnected compact subset of Δ×Δ ⊂ C2.