TY  - JOUR
AU  - Hbil, Jawhar
AU  - Alhazmi, Mofareh
AU  - Zaway, Mohamed
PY  - 2026
TI  - Properties for some Cegrell classes of    m-subharmonic function
JO  - AIMS Mathematics
SP  - 4634
EP  - 4655
VL  - 11
IS  - 2
AB  - 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.
UR  - https://doi.org/10.3934/math.2026188
DO  - 10.3934/math.2026188