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 satisfies certain doubling conditions if and only if 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 de John satisfait certaines conditions de doublement si et seulement si est un domaine semi-uniforme ou un domaine intérieur semi-uniforme.
Keywords: John domain, semi-uniform domain, inner semi-uniform domain, harmonic measure, doubling condition, capacity density condition
Aikawa, Hiroaki 1; Hirata, Kentaro 2
@article{AIF_2008__58_2_429_0, author = {Aikawa, Hiroaki and Hirata, Kentaro}, title = {Doubling conditions for harmonic measure in {John} domains}, journal = {Annales de l'Institut Fourier}, pages = {429--445}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {58}, number = {2}, year = {2008}, doi = {10.5802/aif.2357}, mrnumber = {2410379}, zbl = {1151.31004}, language = {en}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.2357/} }
TY - JOUR AU - Aikawa, Hiroaki AU - Hirata, Kentaro TI - Doubling conditions for harmonic measure in John domains JO - Annales de l'Institut Fourier PY - 2008 SP - 429 EP - 445 VL - 58 IS - 2 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.2357/ DO - 10.5802/aif.2357 LA - en ID - AIF_2008__58_2_429_0 ER -
%0 Journal Article %A Aikawa, Hiroaki %A Hirata, Kentaro %T Doubling conditions for harmonic measure in John domains %J Annales de l'Institut Fourier %D 2008 %P 429-445 %V 58 %N 2 %I Association des Annales de l’institut Fourier %U https://aif.centre-mersenne.org/articles/10.5802/aif.2357/ %R 10.5802/aif.2357 %G en %F AIF_2008__58_2_429_0
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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