Semi-Uniform Domains and the A∞ Property for Harmonic Measure

  title={Semi-Uniform Domains and the A∞ Property for Harmonic Measure},
  author={Jonas Azzam},
  journal={International Mathematics Research Notices},
  • Jonas Azzam
  • Published 8 November 2017
  • Mathematics
  • International Mathematics Research Notices
We study the properties of harmonic measure in semi-uniform domains. Aikawa and Hirata showed in [ 5] that, for John domains satisfying the capacity density condition (CDC), the doubling property for harmonic measure is equivalent to the domain being semi-uniform. Our 1st result removes the John condition by showing that any domain satisfying the CDC whose harmonic measure is doubling is semi-uniform. Next, we develop a substitute for some classical estimates on harmonic measure in… 

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