Some results on Complex m-subharmonic classes

2022/01/18 by Jawher Hbil, Hbil, Jawher, Mohamed Zaway +1
Mathematics · #32W20 #Advanced Topics in Algebra #Complex Variables (math.CV) #FOS: Mathematics #Holomorphic and Operator Theory #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.2201.06851

openalex publication_date 2022/01/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we study the class E_m(Ω) of m-subharmonic functions introduced by Lu in \citeL1. We prove that the convergence in m-capacity implies the convergence of the associated Hessian measure for functions that belong to E_m(Ω). Then we extend those results to the class E_m,χ(Ω) that depends on a given increasing real function χ. A complete characterization of those classes using the Hessian measure is given as well as a subextension theorem relative to E_m,χ(Ω).

Related

• Capacities and Hessians in a class of m-subharmonic functions
• Subextension and approximation of m-subharmonic functions with given boundary values
• Weighted energy class of m-subharmonic functions
• Maximal subextension and approximation of m-subharmonic function
• (m, ψ, δ)-capacity and its properties