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The weak-$A_\infty$
property of harmonic and $p$-harmonic measures implies
uniform rectifiability
Steve Hofmann, Phi Le, José María Martell and Kaj Nyström |
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Vol. 10 (2017), No. 3, 513–558
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Abstract |
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Let , , be an Ahlfors–David regular set of dimension . We show that the weak- property of harmonic measure, for the open set , implies uniform rectifiability of . More generally, we establish a similar result for the Riesz measure, -harmonic measure, associated to the -Laplace operator, . |
Keywords
harmonic measure and $p$-harmonic measure, Poisson kernel,
uniform rectifiability, Carleson measures, Green function,
weak-$A_\infty$
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Mathematical Subject Classification 2010
Primary: 31B05, 31B25, 35J08, 42B25, 42B37
Secondary: 28A75, 28A78
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Milestones
Received: 12 February 2016
Accepted: 12 November 2016
Published: 17 April 2017
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Authors |
| Steve Hofmann | |
| Department of Mathematics University of Missouri Columbia, MO 65211 United States |
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| Phi Le | |
| Mathematics Department Syracuse University 215 Carnegie Building Syracuse, NY 13244 United States |
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| José María Martell | |
| Instituto de Ciencias Matemáticas
CSIC-UAM-UC3M-UCM Consejo Superior de Investigaciones Científicas C/ Nicolás Cabrera, 13-15 E-28049 Madrid Spain |
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| Kaj Nyström | |
| Department of Mathematics Uppsala University SE-751 06 Uppsala Sweden |
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| © 2017 MSP (Mathematical Sciences Publishers). |
