THE WEAK-A∞ PROPERTY OF HARMONIC AND p-HARMONIC MEASURES IMPLIES UNIFORM RECTIFIABILITY

被引：38

作者：

Hofmann, Steve ^{[1
]}

Le, Phi ^{[2
]}

Maria Martell, Jose ^{[3
]}

Nystrom, Kaj ^{[4
]}

机构：

[1] Univ Missouri, Dept Math, Columbia, MO 65211 USA

[2] Syracuse Univ, Math Dept, 215 Carnegie Bldg, Syracuse, NY 13244 USA

[3] CSIC, CSIC, Inst Ciencias Matemat, UAM,UC3M,UCM, C Nicolas Cabrera 13-15, E-28049 Madrid, Spain

[4] Uppsala Univ, Dept Math, SE-75106 Uppsala, Sweden

来源：

ANALYSIS & PDE | 2017年 / 10卷 / 03期

基金：

美国国家科学基金会; 欧洲研究理事会;

关键词：

harmonic measure and p-harmonic measure; Poisson kernel; uniform rectifiability; Carleson measures; Green function; weak-A(infinity); ELLIPTIC-OPERATORS; BOUNDARY-BEHAVIOR; POISSON KERNELS; RIESZ TRANSFORM; REIFENBERG FLAT; REGULARITY;

D O I：

10.2140/apde.2017.10.513

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let E subset of Rn+1, n >= 2, be an Ahlfors-David regular set of dimension n. We show that the weak- A 1 property of harmonic measure, for the open set Omega: =Rn+1 \ E, implies uniform rectifiability of E. More generally, we establish a similar result for the Riesz measure, p-harmonic measure, associated to the p-Laplace operator, 1 < p < infinity.

引用

页码：513 / 558

页数：46

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