Characterizations of p-superharmonic functions on metric spaces
2005 (English)In: Studia Mathematica, ISSN 0039-3223, Vol. 169, no 1, 45-62 p.Article in journal (Refereed) Published
We show the equivalence of some different definitions of p-superharmonic functions given in the literature. We also provide several other characterizations of p-superharmonicity. This is done in complete metric spaces equipped with a doubling measure and supporting a Poincaré inequality. There are many examples of such spaces. A new one given here is the union of a line (with the one-dimensional Lebesgue measure) and a triangle (with a two-dimensional weighted Lebesgue measure). Our results also apply to Cheeger p-superharmonic functions and in the Euclidean setting to A-superharmonic functions, with the usual assumptions on A.
Place, publisher, year, edition, pages
2005. Vol. 169, no 1, 45-62 p.
sueprharmonisk, metriskt rum
IdentifiersURN: urn:nbn:se:liu:diva-23870Local ID: 3407OAI: oai:DiVA.org:liu-23870DiVA: diva2:244185