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

Outi Elina Maasalo; Anna Zatorska-Goldstein

doi:10.4064/cm117-2-10

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

Tom 117 / 2009

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

Streszczenie

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.

Autorzy

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

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