Displaying similar documents to “A Nevanlinna theorem for superharmonic functions on Dirichlet regular Greenian sets”

Characterizations of p-superharmonic functions on metric spaces

Anders Björn (2005)

Studia Mathematica

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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...

Some properties of α-harmonic measure

Dimitrios Betsakos (2008)

Colloquium Mathematicae

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The α-harmonic measure is the hitting distribution of symmetric α-stable processes upon exiting an open set in ℝⁿ (0 < α < 2, n ≥ 2). It can also be defined in the context of Riesz potential theory and the fractional Laplacian. We prove some geometric estimates for α-harmonic measure.