Doubling conditions for harmonic measure in John domains

Aikawa, Hiroaki; Hirata, Kentaro

Annales de l'Institut Fourier, Tome 58 (2008) no. 2, pp. 429-445.

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.

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.

Classification : 31B05, 31B25, 31C35
Mots clés : John domain, semi-uniform domain, inner semi-uniform domain, harmonic measure, doubling condition, capacity density condition

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