The weak-A_∞ property of harmonic and p-harmonic measures implies uniform rectifiability · arXivDesk1511.09270Nov 30, 2015arXiv admin note: substantial text overlap with arXiv:1505.06499
The weak-A∞ property of harmonic and p-harmonic measures implies uniform rectifiability
Steve Hofmann, Phi Le, José María Martell, Kaj Nyström
Abstract
Let E⊂Rn+1, n≥2, be an Ahlfors-David regular set of dimension n. We show that the weak-A∞
property of harmonic measure, for the open set
Ω:=Rn+1∖E , implies uniform rectifiability of
. More generally, we establish a similar result for the Riesz measure,
-harmonic measure, associated to the
-Laplace operator,
.