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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

The logarithm of the Poisson kernel of a $ C\sp{1}$ domain has vanishing mean oscillation


Authors: David S. Jerison and Carlos E. Kenig
Journal: Trans. Amer. Math. Soc. 273 (1982), 781-794
MSC: Primary 31B25; Secondary 42B99
MathSciNet review: 667174
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Abstract: Let $ D$ be a $ {C^1}$ domain in $ {{\mathbf{R}}^n}$, and $ \omega $ the harmonic measure of $ \partial D$, with respect to a fixed pole in $ D$. Then, $ d\omega = kd\sigma $, where $ k$ is the Poisson kernel of $ D$. We show that log $ k$ has vanishing mean oscillation of $ \partial D$.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1982-0667174-2
PII: S 0002-9947(1982)0667174-2
Article copyright: © Copyright 1982 American Mathematical Society