Potential Analysis

, Volume 34, Issue 1, pp 89-100

First online:

A Montel Type Result for Super-Polyharmonic Functions on R N

  • Toshihide FutamuraAffiliated withDepartment of Mathematics, Daido University Email author 
  • , Keiji KitauraAffiliated withDepartment of Mathematics, Graduate School of Science, Hiroshima University
  • , Yoshihiro MizutaAffiliated withDepartment of Mathematics, Hiroshima University

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


Polyharmonic functions Super-polyharmonic functions Spherical means Riesz decomposition

Mathematics Subject Classifications (2010)

Primary 31B30 31B05 31B15