Potential Analysis

, Volume 34, Issue 1, pp 89–100

A Montel Type Result for Super-Polyharmonic Functions on RN

  • Toshihide Futamura
  • Keiji Kitaura
  • Yoshihiro Mizuta

DOI: 10.1007/s11118-010-9183-z

Cite this article as:
Futamura, T., Kitaura, K. & Mizuta, Y. Potential Anal (2011) 34: 89. doi:10.1007/s11118-010-9183-z


Our aim in this paper is to discuss a Montel type result for a family \({\mathcal F}\) of super-polyharmonic functions on RN. We give a condition on spherical means to assure that \({\mathcal F}\) contains a sequence converging outside a set of capacity zero.


Polyharmonic functionsSuper-polyharmonic functionsSpherical meansRiesz decomposition

Mathematics Subject Classifications (2010)

Primary 31B3031B0531B15

Copyright information

© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  • Toshihide Futamura
    • 1
  • Keiji Kitaura
    • 2
  • Yoshihiro Mizuta
    • 3
  1. 1.Department of MathematicsDaido UniversityNagoyaJapan
  2. 2.Department of Mathematics, Graduate School of ScienceHiroshima UniversityHigashi-HiroshimaJapan
  3. 3.Department of MathematicsHiroshima UniversityHigashi-HiroshimaJapan