论文标题
关于本地紧凑空间的能力理论及其与Balayage理论的相互作用
On the theory of capacities on locally compact spaces and its interaction with the theory of balayage
论文作者
论文摘要
本文介绍了局部紧凑空间上的内部（外部）能力理论，相对于一般函数内核，主要重点放在建立内（外部）容量和内部（外部）（外部）（外部）的替代特征的特征上。该分析基本上是基于能力理论与Balayage的紧密相互作用。作为副产品，我们提供了fuglede的内部和外部电容性测量和电容性理论的严格理由（Acta Math。，1960）。即使对于对数，牛顿，绿色，$α$ -RIESZ和$α$ green内核的对数，获得的结果也在很大程度上是新的。
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, $α$-Riesz, and $α$-Green kernels.
