论文标题
一些关于复杂$ m- $ subharmonic课程的结果
Some results on Complex $m-$subharmonic classes
论文作者
论文摘要
在本文中，我们研究了$ m- $ m- $ subharmonic函数的类$ \ Mathcal {e} _ {m}（ω）$，由lu in \ cite {l1}引入。我们证明，$ m $容量的收敛性意味着相关的Hessian度量对属于$ \ Mathcal {e} _ {M}（m}（ω）$的函数的收敛。然后，我们将这些结果扩展到$ \ Mathcal {e} _ {m，χ}（ω）$，取决于给定增加的实际函数$χ$。使用Hessian度量对这些类的完整表征以及相对于$ \ MATHCAL {E} _ {M，χ}（ω）$的子扩展定理。
In this paper we study the class $\mathcal{E}_{m}(Ω)$ 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 $\mathcal{E}_{m}(Ω)$. Then we extend those results to the class $\mathcal{E}_{m,χ}(Ω)$ 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 $\mathcal{E}_{m,χ}(Ω)$.
