Arkiv för Matematik

  • Ark. Mat.
  • Volume 55, Number 1 (2017), 229-241.

A note on approximation of plurisubharmonic functions

Håkan Persson and Jan Wiegerinck

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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 $\overline{\Omega}$, with functions that are plurisubharmonic on (shrinking) neighborhoods of $\overline{\Omega}$. We show that such approximation is possible if the boundary of $\Omega$ is $C^0$ outside a countable exceptional set $E \subset \partial \Omega$. 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.

Article information

Ark. Mat., Volume 55, Number 1 (2017), 229-241.

Received: 5 October 2016
Revised: 27 January 2017
First available in Project Euclid: 2 February 2018

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 32U05: Plurisubharmonic functions and generalizations [See also 31C10]
Secondary: 31B05: Harmonic, subharmonic, superharmonic functions 31B25: Boundary behavior

plurisubharmonic function approximation Mergelyan type approximation


Persson, Håkan; Wiegerinck, Jan. A note on approximation of plurisubharmonic functions. Ark. Mat. 55 (2017), no. 1, 229--241. doi:10.4310/ARKIV.2017.v55.n1.a12.

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