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Martin Boundary of a Fine Domain and a Fatou-Naïm-Doob Theorem for Finely Superharmonic Functions

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We construct the Martin compactification U ¯ ¯ ¯ ¯    of a fine domain U in R n (n = 2) and the Riesz-Martin kernel K on U×U ¯ ¯ ¯ ¯    . We obtain the integral representation of finely superharmonic fonctions ≥ 0 on U in terms of K and establish the Fatou-Naim-Doob theorem in this setting.
OriginalsprogEngelsk
TidsskriftPotential Analysis
Vol/bind44
Udgave nummer1
Sider (fra-til)1-25
ISSN0926-2601
DOI
StatusUdgivet - 2016

ID: 142181860