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

Mohamed  El Kadiri; Bent Fuglede

doi:10.1007/s11118-015-9495-0

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

Mohamed El Kadiri, Bent Fuglede

Institut for Matematiske Fag

2 Citationer (Scopus)

Abstract

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.

Originalsprog	Engelsk
Tidsskrift	Potential Analysis
Vol/bind	44
Udgave nummer	1
Sider (fra-til)	1-25
ISSN	0926-2601
DOI	https://doi.org/10.1007/s11118-015-9495-0
Status	Udgivet - 1 jan. 2016

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10.1007/s11118-015-9495-0

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abstract = "We construct the Martin compactification (Formula presented.) of a fine domain U in Rn (n = 2) and the Riesz-Martin kernel K on (Formula presented.). 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.",

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T1 - Martin Boundary of a Fine Domain and a Fatou-Naïm-Doob Theorem for Finely Superharmonic Functions

AU - El Kadiri, Mohamed

AU - Fuglede, Bent

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N2 - We construct the Martin compactification (Formula presented.) of a fine domain U in Rn (n = 2) and the Riesz-Martin kernel K on (Formula presented.). 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.

AB - We construct the Martin compactification (Formula presented.) of a fine domain U in Rn (n = 2) and the Riesz-Martin kernel K on (Formula presented.). 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.

U2 - 10.1007/s11118-015-9495-0

DO - 10.1007/s11118-015-9495-0

M3 - Journal article

SN - 0926-2601

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SP - 1

EP - 25

JO - Potential Analysis

JF - Potential Analysis

IS - 1

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

Abstract

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