Hyperconvex domain

In this paper, we shall construct a new class of weighted energy functions in the class of m-subharmonic functions and study some analysis properties of this class. Specifically, the paper is organized as follows.

7p viharry 15-12-2022 14 3   Download

The aim of this article "Weak tautness and hyperconvexity in Hilbert spaces" is to introduce the notions of weak tautness and hyperconvexity of a domain in a Banach space and to establish the relation between them. Moreover, some conditions under which a balanced domain in a Hilbert space and a Hartogs domain in a Banach space are hyperconvex are also given.

14p runordie5 04-07-2022 4 1   Download

In the paper "Some properties of Reinhardt domains", the authors establish the equivalence between hyperconvexity of a fat bounded Reinhardt domain and the existence of a Stein neighbourhood basis of its closure. Next, the authors give a necessary and sufficient condition on a bounded Reinhardt domain D so that every holomorphic mapping from the punctured disk ∆∗ into D can be extended holomorphically to a map from ∆ into D.

15p runordie5 04-07-2022 9 2   Download

In this article "Convergence in capacity and applications", the authors prove that if uj , vj , w ∈ E () such that uj , vj ≥ w, ∀ j ≥ 1, and |uj − vj | → 0 in Cn-capacity, then limj→∞ h(ϕ1,...,ϕm)[(ddcuj )n − (ddcvj )n] = 0 in the weak-topology of measures for all ϕ1,...,ϕm ∈ PSH ∩L∞ loc(), h ∈ C(Rm). We shall then use this result to give some applications.

13p runordie5 04-07-2022 8 2   Download

In the paper "The complex Monge–Ampère equation in unbounded hyperconvex domains in Cn", we look for solutions of the complex Monge–Ampère equation with boundary values (ddcu)n = μ in an unbounded hyperconvex domain of Cn.

18p runordie3 27-06-2022 15 3   Download

In this paper "The locally F-approximation property of bounded hyperconvex domains", we study the local property of bounded hyperconvex domains Ω which we can approximate each plurisubharmonic function u ∈ F(Ω) by an increasing sequence of plurisubharmonic functions defined on strictly larger domains.

7p runordie3 27-06-2022 16 2   Download

In the first part of this study, we characterize the compact subspaces of Hpu(Bp) and their relation to the vanishing Carleson measures. In the second part, we discuss the dual complement of the complex ellipsoid and give a duality result for Hpu(Bp)spaces in the sense of Grothendieck–Köthe–da Silva.

9p nutifooddau 21-01-2019 13 1   Download