The logarithm of the Poisson kernel of a 𝐶¹ domain has vanishing mean oscillation

Jerison, David S.; Kenig, Carlos E.

doi:10.1090/S0002-9947-1982-0667174-2

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
DOI: https://doi.org/10.1090/S0002-9947-1982-0667174-2
MathSciNet review: 667174
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Abstract: Let be a ${C^1}$ domain in ${{\mathbf{R}}^n}$ , and $\omega$ the harmonic measure of $\partial D$ , with respect to a fixed pole in . Then, $d\omega = kd\sigma$ , where is the Poisson kernel of . We show that log has vanishing mean oscillation of $\partial D$ .

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