Two criterions of Wiener type for minimally thin sets and rarefied sets in a cone Dedicated to Professor Masayuki Ito on his 60th birthday

Ikuko MIYAMOTO; Hidenobu YOSHIDA

doi:10.2969/jmsj/1191593906

Journal of the Mathematical Society of Japan

Online ISSN : 1881-1167
Print ISSN : 0025-5645
ISSN-L : 0025-5645

Two criterions of Wiener type for minimally thin sets and rarefied sets in a cone

Dedicated to Professor Masayuki Ito on his 60th birthday

Ikuko MIYAMOTO, Hidenobu YOSHIDA

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Keywords: Superharmonic functions, cones, rarefied sets

JOURNAL FREE ACCESS

2002 Volume 54 Issue 3 Pages 487-512

DOI https://doi.org/10.2969/jmsj/1191593906

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Abstract

We shall give two criterions of Wiener type which characterize minimally thin sets and rarefied sets in a cone. We shall also show that a positive superharmonic function on a cone behaves regularly outside a rarefied set in a cone. These facts are known for a half space which is a special cone.

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