On the Theory of Capacities on Locally Compact Spaces and its Interaction with the Theory of Balayage

被引：8
作者：
Zorii, Natalia [1 ]
机构：
[1] Natl Acad Sci Ukraine, Inst Math, Tereshchenkivska 3, UA-01601 Kiev 4, Ukraine
来源：
POTENTIAL ANALYSIS | 2023年 / 59卷 / 03期
关键词：
Inner and outer capacities and capacitary measures; Inner and outer balayage; Capacitability; Perfect kernels; Maximum principles; Principle of positivity of mass; POTENTIALS;
D O I：
10.1007/s11118-022-10010-3
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
The paper deals with the theory of inner (outer) capacities on locally compact spaces with respect to general function kernels, the main emphasis being placed on the establishment of alternative characterizations of inner (outer) capacities and inner (outer) capacitary measures for arbitrary sets. The analysis is substantially based on the close interaction between the theory of capacities and that of balayage. As a by-product, we provide a rigorous justification of Fuglede's theories of inner and outer capacitary measures and capacitability (Acta Math., 1960). The results obtained are largely new even for the logarithmic, Newtonian, Green, alpha-Riesz, and alpha-Green kernels.
引用
收藏
页码：1345 / 1379
页数：35
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