ポテンシャル論的Kernelについての注意

Abstract

In the preceding paper [4], we treated the characterization of the family of potential theoretic measures G+ (Φ) . Generally considering the characterization of the family G+ (Φ), we defined a concept "T-kernel" and proved that Newtonian kernel Φ_N and the kernel Φ_w associated with the heat equation are T-kernels. The present paper deals with two remarks on potential theoretic kernels which have continuous potentials ; the first is concerned with T-kernel and the second is done with the domination principles for Φ_w-potential. In the first section we shall remark that α-kernel and Green kernel are also T-kernels. In the second section we shall introduce a definition of C-domination principle and we shall prove that the kernel Φ_w does not satisfy the ordinary domination principle but it satisfies the C-domination principle.