A note on approximation of plurisubharmonic functions

Håkan Persson Uppsala University Jan Wiegerinck University of Amsterdam

Complex Variables and Complex Analysis Functional Analysis mathscidoc:1803.43018

Arkiv for Matematik, 55, 2017
We extend a recent result of Avelin, Hed, and Persson about approximation of functions f that are plurisubharmonic on a domain Ω and continuous on ˙Ω, with functions that are plurisubharmonic on (shrinking) neighborhoods of ˙Ω. We show that such approximation is possible if the boundary of Ω is C0 outside a countable exceptional set E⊂∂Ω. In particular, approximation is possible on the Hartogs triangle. For Hölder 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 Hölder continuous case is possible.
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  title={A note on approximation of plurisubharmonic functions},
  author={Håkan Persson, and Jan Wiegerinck},
  booktitle={Arkiv for Matematik},
Håkan Persson, and Jan Wiegerinck. A note on approximation of plurisubharmonic functions. 2017. Vol. 55. In Arkiv for Matematik. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20180301171632063796953.
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