Some results on Complex $m-$subharmonic classes

Abstract

In this paper we study the class ${\mathcal{E}}_m(\Omega )$ of $m-$subharmonic functions introduced by Lu in \cite{L1}. We prove that the convergence in $m-$capacity implies the convergence of the associated Hessian measure for functions that belong to ${\mathcal{E}}_m(\Omega )$. Then we extend those results to the class ${\mathcal{E}}_{m,\chi }(\Omega )$ that depends on a given increasing real function $\chi$. A complete characterization of those classes using the Hessian measure is given as well as a subextension theorem relative to ${\mathcal{E}}_{m,\chi }(\Omega )$.

arXiv comment17