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

被引：2

作者：

El Kadiri, Mohamed ^{[1
]}

Fuglede, Bent ^{[2
]}

机构：

[1] Univ Mohammed 5, Fac Sci, Dept Math, BP 1014, Rabat, Morocco

[2] Dept Math Sci, Univ Pk 5, DK-2100 Copenhagen, Denmark

来源：

POTENTIAL ANALYSIS | 2016年 / 44卷 / 01期

关键词：

Martin boundary; Integral representation; Riesz-Martin kernel; Finely superharmonic function; Finely harmonic function; INTEGRAL-REPRESENTATION; RIESZ-DECOMPOSITION;

D O I：

10.1007/s11118-015-9495-0

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We construct the Martin compactification (u) over bar of a fine domain U in R (n) (n = 2) and the Riesz-Martin kernel K on U x (u) over bar . 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.

引用

页码：1 / 25

页数：25

共 30 条

[1] Aikawa H, 2012, CRM PROC & LECT NOTE, V55, P235
[2] Alfsen E.M., 2001, ERGEBNISSE MATH, V57
[3] ANCONA A, 1984, LECT NOTES MATH, V1096, P34
[4] [Anonymous], 1972, Potential Theory on Harmonic Spaces
[5] ARMITAGE DH, 2001, SPRINGER MG MATH, P1, DOI 10.1007/978-1-4471-0233-5
[6] On the tightness of capacities associated with sub-Markovian resolvents
Beznea, L
Boboc, N
[J]. BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, 2005, 37 : 899 - 907
[7] Boboc N., 1985, REV ROUMAINE MATH PU, V30, P1
[8] Boboc N., 1981, LECT NOTES MATH, V853
[9] DELLACHERIE C, 1987, PROBABILITES POTENTI, pCH12
[10] Doob J. L., 1984, Classical Potential Theory and its Probabilistic Counterpart, V262

← 1 2 3 →