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| On the Cegrell Classes Associated to a Positive Closed Current |
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Citation： |
Mohamed ZAWAY.On the Cegrell Classes Associated to a Positive Closed Current[J].Chinese Annals of Mathematics B,2019,40(4):567~584 |
| Page view： 1596
Net amount： 1381 |
Authors： |
Mohamed ZAWAY; |
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| Abstract： |
The aim of this paper is to study the operator
$(dd^c\centerdot)^q\wedge T$ on some classes of plurisubharmonic
(psh) functions, which are not necessary bounded, where $T$ is a
positive closed current of bidimension $(q,q)$ on an open set
$\Omega$ of $\Bbb C^n$. The author introduces two classes
$\mathcal{F}_{p}^{T}(\Omega)$ and $\mathcal{E}_p^T(\Omega)$ and
shows first that they belong to the domain of definition of the
operator $(dd^c\centerdot)^q\wedge T$. Then the author proves that
all functions that belong to these classes are
$C_T$-quasi-continuous and that the comparison principle is valid
for them. |
Keywords： |
Positive closed current, Plurisubharmonic function, Capacity,Monge-Amp`ere Operator |
Classification： |
32U40, 32U05, 32U20 |
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