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A criterion on a subdomain of the disc for its harmonic measure to be comparable with Lebesgue measure


Author: A. L. VolЬberg
Journal: Proc. Amer. Math. Soc. 112 (1991), 153-162
MSC: Primary 31A15; Secondary 30C85
DOI: https://doi.org/10.1090/S0002-9939-1991-1045152-2
MathSciNet review: 1045152
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Abstract: A subdomain $ O$ of the disc $ \mathbb{D}$ is called a boundary layer if $ \omega (O, \cdot ) \geq \alpha \cdot m$, where $ \omega (O, \cdot )$ is the harmonic measure of $ O$. The metric criterion in terms of $ \partial O$ is given for the case when $ \alpha $ is near 1.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1991-1045152-2
Article copyright: © Copyright 1991 American Mathematical Society