an:00006862
Zbl 0758.42008
David, Guy; Jerison, D.
Lipschitz approximation to hypersurfaces, harmonic measure, and singular integrals
EN
Indiana Univ. Math. J. 39, No. 3, 831-845 (1990).
00156119
1990
j
42B20
Lipschitz approximation; hypersurfaces satisfying a scale-invariant condition; singular integral; harmonic measure; surface measure
The authors study hypersurfaces satisfying a scale-invariant condition. This condition is a generalization of the chord-arc condition on planar domains. Theorem 1 shows that, at all scales, a large fraction of such a surface coincides with a Lipschitz graph. As a consequence of this result, it is shown that a singular integral operator on a surface is bounded. It is also pointed out that an NTA domain satisfies an analogous property. As a consequence of this fact, it is deduced that harmonic measure and surface measure are mutually absolutely continuous.
T.Murai (Nagoya)