Characterizations of $p$-superharmonic functions on metric spaces

Anders Björn ¹

¹ Department of Mathematics Linköpings universitet SE-581 83 Linköping, Sweden

Studia Mathematica, Tome 169 (2005) no. 1, pp. 45-62

Résumé

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 $\cal A$-superharmonic functions, with the usual assumptions on $\cal A$.

Détail

DOI : 10.4064/sm169-1-3

Keywords: equivalence different definitions p superharmonic functions given literature provide several other characterizations p superharmonicity done complete metric spaces equipped doubling measure supporting poincar inequality there many examples spaces given here union line one dimensional lebesgue measure triangle two dimensional weighted lebesgue measure results apply cheeger p superharmonic functions euclidean setting cal a superharmonic functions usual assumptions cal