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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm169-1-3,
author = {Anders Bj\"orn},
title = {Characterizations of p-superharmonic functions on metric spaces},
journal = {Studia Mathematica},
volume = {166},
year = {2005},
pages = {45-62},
zbl = {1079.31006},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm169-1-3}
}
Anders Björn. Characterizations of p-superharmonic functions on metric spaces. Studia Mathematica, Tome 166 (2005) pp. 45-62. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm169-1-3/