Doubling conditions for harmonic measure in John domains

Hiroaki Aikawa[1]; Kentaro Hirata[2]

  • [1] Hokkaido University Department of Mathematics Sapporo 060-0810 (Japan)
  • [2] Akita University Faculty of Education and Human Studies Akita 010-8502 (Japan)

Annales de l’institut Fourier (2008)

  • Volume: 58, Issue: 2, page 429-445
  • ISSN: 0373-0956

Abstract

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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.

How to cite

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Aikawa, Hiroaki, and Hirata, Kentaro. "Doubling conditions for harmonic measure in John domains." Annales de l’institut Fourier 58.2 (2008): 429-445. <http://eudml.org/doc/10321>.

@article{Aikawa2008,
abstract = {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.},
affiliation = {Hokkaido University Department of Mathematics Sapporo 060-0810 (Japan); Akita University Faculty of Education and Human Studies Akita 010-8502 (Japan)},
author = {Aikawa, Hiroaki, Hirata, Kentaro},
journal = {Annales de l’institut Fourier},
keywords = {John domain; semi-uniform domain; inner semi-uniform domain; harmonic measure; doubling condition; capacity density condition; capacity, density condition},
language = {eng},
number = {2},
pages = {429-445},
publisher = {Association des Annales de l’institut Fourier},
title = {Doubling conditions for harmonic measure in John domains},
url = {http://eudml.org/doc/10321},
volume = {58},
year = {2008},
}

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
PB - Association des Annales de l’institut Fourier
VL - 58
IS - 2
SP - 429
EP - 445
AB - 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.
LA - eng
KW - John domain; semi-uniform domain; inner semi-uniform domain; harmonic measure; doubling condition; capacity density condition; capacity, density condition
UR - http://eudml.org/doc/10321
ER -

References

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  13. D. S. Jerison, C. E. Kenig, Boundary behavior of harmonic functions in nontangentially accessible domains, Adv. in Math. 46 (1982), 80-147 Zbl0514.31003MR676988
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