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arXiv · 1403.0857

Martin boundary of a fine domain and a Fatou-Naim-Doob theorem for finely superharmonic functions

Mohamed El Kadiri·Bent Fuglede
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Abstract

We construct the Martin compactification ${\bar U}$ of a fine domain $U$ in $R^n$, $n\ge 2$, and the Riesz-Martin kernel $K$ on $U \times{\bar U}$. We obtain the integral representation of finely superharmonic fonctions $\ge 0$ on $U$ in terms of $K$ and establish the Fatou-Naim-Doob theorem in this setting.

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Mohamed El Kadiri, Bent Fuglede. 2014-03-04. Martin boundary of a fine domain and a Fatou-Naim-Doob theorem for finely superharmonic functions. https://arxiv.org/abs/1403.0857

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