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A note on approximation of plurisubharmonic functions
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
Univ Amsterdam, KdV Inst Math, Sci Pk 105-107,POB 94248, NL-1090 GE Amsterdam, Netherlands..
2017 (English)In: Arkiv för matematik, ISSN 0004-2080, E-ISSN 1871-2487, Vol. 55, no 1, p. 229-241Article in journal (Refereed) Published
Abstract [en]

We extend a recent result of Avelin, Hed, and Persson about approximation of functions f that are plurisubharmonic on a domain Omega and continuous on (Omega) over bar, with functions that are plurisubharmonic on (shrinking) neighborhoods of (Omega) over bar We show that such approximation is possible if the boundary of Omega is C-0 outside a countable exceptional set E subset of partial derivative Omega. In particular, approximation is possible on the Hartogs triangle. For Holder continuous u, approximation is possible under less restrictive conditions on E. We next give examples of domains where this kind of approximation is not possible, even when approximation in the Holder continuous case is possible.

Place, publisher, year, edition, pages
INT PRESS BOSTON, INC , 2017. Vol. 55, no 1, p. 229-241
Keywords [en]
plurisubharmonic function, approximation, Mergelyan type approximation
National Category
Mathematics
Identifiers
URN: urn:nbn:se:uu:diva-347270DOI: 10.4310/ARKIV.2017.v55.n1.a12ISI: 000424524100012OAI: oai:DiVA.org:uu-347270DiVA, id: diva2:1193926
Available from: 2018-03-28 Created: 2018-03-28 Last updated: 2018-03-28Bibliographically approved

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