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

Outi Elina Maasalo; Anna Zatorska-Goldstein — 2009

Colloquium Mathematicae

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.

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