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1 June 2014 Uniform rectifiability and harmonic measure, II: Poisson kernels in Lp imply uniform rectifiability
Steve Hofmann, José María Martell, Ignacio Uriarte-Tuero
Duke Math. J. 163(8): 1601-1654 (1 June 2014). DOI: 10.1215/00127094-2713809

Abstract

We present the converse to a higher-dimensional, scale-invariant version of the classical F. and M. Riesz theorem, proved by the first two authors. More precisely, for n2, for an Ahlfors–David regular domain ΩRn+1 which satisfies the Harnack chain condition plus an interior (but not exterior) corkscrew condition, we show that absolute continuity of the harmonic measure with respect to the surface measure on Ω, with scale-invariant higher integrability of the Poisson kernel, is sufficient to imply quantitative rectifiability of Ω.

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Steve Hofmann. José María Martell. Ignacio Uriarte-Tuero. "Uniform rectifiability and harmonic measure, II: Poisson kernels in Lp imply uniform rectifiability." Duke Math. J. 163 (8) 1601 - 1654, 1 June 2014. https://doi.org/10.1215/00127094-2713809

Information

Published: 1 June 2014
First available in Project Euclid: 26 May 2014

zbMATH: 1323.31008
MathSciNet: MR3210969
Digital Object Identifier: 10.1215/00127094-2713809

Subjects:
Primary: 31B05
Secondary: 35J08 , 35J25 , 42B25 , 42B37 , 42B99

Rights: Copyright © 2014 Duke University Press

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Vol.163 • No. 8 • 1 June 2014
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