Maximal Plurifinely Plurisubharmonic Functions

被引：20
|
作者：
El Kadiri, Mohamed [1 ]
Smit, Iris M. [2 ]
机构：
[1] Univ Mohammed V Agdal, Dept Math, Fac Sci, Rabat, Morocco
[2] Univ Amsterdam, KdV Inst Math, NL-1090 GE Amsterdam, Netherlands
来源：
POTENTIAL ANALYSIS | 2014年 / 41卷 / 04期
关键词：
Maximal plurisubharmonic functions; Plurifinely plurisubharmonic functions; Monge-Ampere operator; INTEGRAL-REPRESENTATION; FINE TOPOLOGY;
D O I：
10.1007/s11118-014-9421-x
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
The main purpose of this paper is to introduce and study the notion of -maximal -plurisubharmonic functions, which extends the notion of maximal plurisubharmonic functions on a Euclidean domain to an -domain of a", (n) in a natural way. Our main result is that a finite -plurisubharmonic function u on a plurifine domain U satisfies (d d (c) u) (n) = 0 if and only if u is -locally -maximal outside some pluripolar set. In particular, a finite -maximal plurisubharmonic function u satisfies (d d (c) u) (n) = 0.
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页码：1329 / 1345
页数：17
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