Potential Analysis

, Volume 1, Issue 2, pp 133–140 | Cite as

Removability of polar sets for harmonic functions

  • Ursula Schirmeier
Article
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Abstract

A classical result of G. Bouligand states that bounded harmonic functions can be extended across closed polar sets. F.-Y. Maeda replaced the boundedness assumption by the condition of energy finiteness for harmonic spaces with Green function.

This paper proves this result for generalP-harmonic spaces and shows that the extension property for a harmonic functionu and the condition of energy finiteness are equivalent to a majorization property foru 2 .

Mathematics Subject Classification (1991)

31D05 

Key words

Potential theory polar set removability extension theorem harmonic space 
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Copyright information

© Kluwer Academic Publishers 1992

Authors and Affiliations

  • Ursula Schirmeier
    • 1
  1. 1.Math.-Geogr. Fakultät der Katholischen Universität EichstättEichstättGermany

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