Maximal subextension and approximation of $m-$subharmonic function

TL;DR

This paper investigates subextensions and approximation methods for m-subharmonic functions within specific functional classes, advancing understanding of their properties and potential applications.

Contribution

It introduces new results on subextensions and approximation techniques for m-subharmonic functions in the classes \(\\mathcal{F}_m(\Omega)\) and \(\mathcal{E}_{m,\chi}(\Omega)\).

Findings

Established new subextension results for m-subharmonic functions.

Developed approximation methods within the classes \(\mathcal{F}_m(\Omega)\) and \(\mathcal{E}_{m,\chi}(\Omega)\).

Enhanced theoretical understanding of m-subharmonic function classes.

Abstract

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