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

Department of Mathematical Sciences

2 Citations (Scopus)

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.

Original language	English
Journal	Potential Analysis
Volume	44
Issue number	1
Pages (from-to)	1-25
ISSN	0926-2601
DOIs	https://doi.org/10.1007/s11118-015-9495-0
Publication status	Published - 1 Jan 2016

Access to Document

10.1007/s11118-015-9495-0

Cite this

@article{9e63e811adda4d5d88979874d55884ea,

title = "Martin Boundary of a Fine Domain and a Fatou-Na{\"i}m-Doob Theorem for Finely Superharmonic Functions",

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.",

author = "{El Kadiri}, Mohamed and Bent Fuglede",

year = "2016",

month = jan,

day = "1",

doi = "10.1007/s11118-015-9495-0",

language = "English",

volume = "44",

pages = "1--25",

journal = "Potential Analysis",

issn = "0926-2601",

publisher = "Springer",

number = "1",

}

TY - JOUR

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

AU - El Kadiri, Mohamed

AU - Fuglede, Bent

PY - 2016/1/1

Y1 - 2016/1/1

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

VL - 44

SP - 1

EP - 25

JO - Potential Analysis

JF - Potential Analysis

IS - 1

ER -

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

Abstract

Access to Document

Fingerprint

Cite this