Journal article
On the Cegrell classes

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Author list: Åhag, Per
Publication year: 2007
Start page: 243
End page: 264
Number of pages: 22
ISSN: 0025-5874
View additional information: View in Web of Science™

Abstract

The Cegrell classes with zero boundary data are defined by certain decreasing approximating sequences of functions with different properties depending on the class in question. It is different for Cegrell classes which are given by a continuous function f, these classes are defined by an inequality. It is proved in this article that it is possible to define the Cegrell classes which are given by f in a similar manner as those classes with zero boundary data. An existence result for the Dirichlet problem for certain singular measures is proved. The article ends with three applications. Results connected to convergence in capacity, subextension of plurisubharmonic functions and integrability are proved.


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