Riesz potentials and p-superharmonic functions in Lie groups of Heisenberg type

Nicola Garofalo, Jeremy T. Tyson

Research output: Contribution to journalArticlepeer-review

Abstract

We prove a superposition principle for Riesz potentials of nonnegative continuous functions on Lie groups of Heisenberg type. More precisely, we show that the Riesz potential R α(ρ)(g)=∫ GN(g -1g') α-Qρ(g')dg' of a nonnegative function C0() on a group of Heisenberg type is necessarily either p-subharmonic or p-superharmonic, depending on p and. Here N denotes the anisotropic homogeneous norm on such groups introduced by Kaplan. This result extends to a wide class of nonabelian stratified Lie groups a recent remarkable superposition result of Crandall and Zhang.

Original languageEnglish (US)
Pages (from-to)353-366
Number of pages14
JournalBulletin of the London Mathematical Society
Volume44
Issue number2
DOIs
StatePublished - Apr 2012

ASJC Scopus subject areas

  • Mathematics(all)

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