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Characterizations of p-superharmonic functions on metric spaces

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Björn A.

Studia Mathematica

2005

tom 169

nr 1

45-62

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.

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1 Studia Mathematica

1 Björn A.

1 2005

Wyniki wyszukiwania

Characterizations of p-superharmonic functions on metric spaces