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Jawhar Hbil,
Complex m-subharmonic classes.
Int. J. Math. Comput. Sci., 20, no. 4, (2025), 1145-1157.

DOI:

https://doi.org/10.69793/ijmcs/04.2025/jawhar

Keywords and phrases:

m-subharmonic function, Capacity, Hessian operator, Convergence in m-capacity.

Abstract:

In this paper, we associate to every m-positive closed current R and to any weight \chi, defined on a domain \Omega\subset \mathbb{C}^n, a new class of m-subharmonic functions called E_{R,\chi,m}(\Omega). We prove that the Hessian operator is well defined on this class and we characterize the behavior near \partial \Omega of the function that belongs to E_{R,\chi,m}(\Omega).