Doubling conditions for harmonic measure in John domains
Annales de l'Institut Fourier, Volume 58 (2008) no. 2, pp. 429-445.

We introduce new classes of domains, i.e., semi-uniform domains and inner semi-uniform domains. Both of them are intermediate between the class of John domains and the class of uniform domains. Under the capacity density condition, we show that the harmonic measure of a John domain D satisfies certain doubling conditions if and only if D is a semi-uniform domain or an inner semi-uniform domain.

Nous introduisons des classes nouvelles de domaines, domaines semi-uniformes et domaines intérieurs semi-uniformes. Elles sont intermédiaires entre la classe des domaines de John et la classe des domaines uniformes. Sous la condition de densité de capacité, nous prouvons que la mesure harmonique d’un domaine D de John satisfait certaines conditions de doublement si et seulement si D est un domaine semi-uniforme ou un domaine intérieur semi-uniforme.

DOI: 10.5802/aif.2357
Classification: 31B05,  31B25,  31C35
Keywords: John domain, semi-uniform domain, inner semi-uniform domain, harmonic measure, doubling condition, capacity density condition
Aikawa, Hiroaki 1; Hirata, Kentaro 2

1 Hokkaido University Department of Mathematics Sapporo 060-0810 (Japan)
2 Akita University Faculty of Education and Human Studies Akita 010-8502 (Japan)
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Aikawa, Hiroaki; Hirata, Kentaro. Doubling conditions for harmonic measure in John domains. Annales de l'Institut Fourier, Volume 58 (2008) no. 2, pp. 429-445. doi : 10.5802/aif.2357. https://aif.centre-mersenne.org/articles/10.5802/aif.2357/

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