@article{Hbil2026, 
author = {Jawhar Hbil and Mofareh Alhazmi and Mohamed Zaway},
title = {Properties for some Cegrell classes of    m-subharmonic function},
year = {2026},
journal = {AIMS Mathematics},
volume = {11},
number = {2},
pages = {4634-4655},
keywords = {m-subharmonic functions, complex Hessian operator, maximal subextension, Cegrell classes, Lelong numbers, capacity convergence},
url = {https://www.sciopen.com/article/10.3934/math.2026188},
doi = {10.3934/math.2026188},
abstract = {This paper investigated the properties of maximal subextensions for    m-subharmonic (   m-sh) functions in the context of complex Hessian operators. We established three main theorems that significantly advance the theory. First, we provided a complete characterization of maximal subextensions in the class              F        m    a    (  Ω  ), showing that any subextension satisfying a minimality condition on its Hessian mass must coincide with the maximal subextension. Second, we proved that for functions in              E        m    (  Ω  ), the maximal subextension relates to the original function through an    m-maximal function and preserves Lelong numbers. Third, we demonstrated convergence stability, proving that for sequences with boundary values in              F        m    (  Ω  ,  f  ) converging in        L          loc        1   and uniformly bounded below, their maximal subextensions converged to the maximal subextension of the limit function.}
}