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Maximal subextension and approximation of $m-$subharmonic function

Nguyen Van Phu, Nguyen Quang Dieu

Abstract

In this paper, we first study subextensions in the classes $\mathcal{F}_{m}(Ω)$ and $\mathcal{E}_{m,χ}(Ω)$. These results are then used to study approximation in the classes $\mathcal{F}_{m}(Ω)$ and $\mathcal{E}_{m,χ}(Ω)$.

Maximal subextension and approximation of $m-$subharmonic function

Abstract

In this paper, we first study subextensions in the classes and . These results are then used to study approximation in the classes and .
Paper Structure (4 sections, 10 theorems, 88 equations)

This paper contains 4 sections, 10 theorems, 88 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Subextension in the class $\mathcal{E}_{m,\chi}$
  4. Approximation in $\mathcal{F}_m$ and $\mathcal{E}_{m,\chi}$

Key Result

Proposition 2.3

Let $\Omega$ be an open set in $\mathbb C^n$. Then the following assertions hold true: (1) If $u,v\in SH_{m}(\Omega)$ then $au+bv \in SH_{m}(\Omega)$ for any $a,b\geq 0.$ (2) $PSH(\Omega)= SH_{n}(\Omega)\subset \cdots\subset SH_{1}(\Omega)=SH(\Omega).$ (3) If $u\in SH_{m}(\Omega)$ then a standard ap

Theorems & Definitions (24)

  • Definition 2.1
  • Example 2.2
  • Proposition 2.3
  • Definition 2.4
  • Example 2.5
  • Definition 2.6
  • Lemma 2.7
  • proof
  • Lemma 3.1
  • proof
  • ...and 14 more