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On the Cegrell classes
Mid Sweden University, Faculty of Science, Technology and Media, Department of Engineering, Physics and Mathematics.
Jagiellonian University, Poland.
2007 (English)In: Mathematische Zeitschrift, ISSN 0025-5874, E-ISSN 1432-1823, Vol. 256, no 2, p. 243-264Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
2007. Vol. 256, no 2, p. 243-264
Keywords [en]
Complex Monge-Ampère operator, Dirichlet problem, Plurisubharmonic function
National Category
Mathematics
Identifiers
URN: urn:nbn:se:miun:diva-8464DOI: 10.1007/s00209-006-0067-2ISI: 000245854600002Scopus ID: 2-s2.0-33947326069OAI: oai:DiVA.org:miun-8464DiVA, id: diva2:139824
Available from: 2009-01-26 Created: 2009-01-26 Last updated: 2017-12-14Bibliographically approved

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Åhag, Per

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