A note on global integrability of upper gradients of $p$-superharmonic functions

Volume 117 / 2009

Outi Elina Maasalo, Anna Zatorska-Goldstein Colloquium Mathematicum 117 (2009), 281-288 MSC: 31C45, 49N60. DOI: 10.4064/cm117-2-10


We consider a complete metric space equipped with a doubling measure and a weak Poincaré inequality. We prove that for all $p$-superharmonic functions there exists an upper gradient that is integrable on $H$-chain sets with a positive exponent.


  • Outi Elina MaasaloInstitute of Mathematics
    Helsinki University of Technology
    P.O. Box 1100
    FI-02015 TKK, Finland
  • Anna Zatorska-GoldsteinInstitute of Applied Mathematics and Mechanics
    University of Warsaw
    Banacha 2
    PL-02-097 Warszawa, Poland

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