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The weak-A∞ PROPERTY OF HARMONIC AND p-HARMONIC MEASURES IMPLIES UNIFORM RECTIFIABILITY
Univ Missouri, Dept Math, Columbia, MO 65211 USA..
Syracuse Univ, Math Dept, 215 Carnegie Bldg, Syracuse, NY 13244 USA..
CSIC, CSIC, Inst Ciencias Matemat, UAM,UC3M,UCM, C Nicolas Cabrera 13-15, E-28049 Madrid, Spain..
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Probability Theory.
2017 (English)In: Analysis & PDE, ISSN 2157-5045, E-ISSN 1948-206X, Vol. 10, no 3, 513-558 p.Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
MATHEMATICAL SCIENCE PUBL , 2017. Vol. 10, no 3, 513-558 p.
Keyword [en]
harmonic measure and p-harmonic measure, Poisson kernel, uniform rectifiability, Carleson measures, Green function, weak-A(infinity)
National Category
Mathematical Analysis
Identifiers
URN: urn:nbn:se:uu:diva-328276DOI: 10.2140/apde.2017.10.513ISI: 000403096000001OAI: oai:DiVA.org:uu-328276DiVA: diva2:1156414
Available from: 2017-11-13 Created: 2017-11-13 Last updated: 2017-11-13Bibliographically approved

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Nyström, Kaj

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