Uniform Rectifiability and Harmonic Measure III: Riesz Transform Bounds Imply Uniform Rectifiability of Boundaries of 1-sided NTA Domains

Steve Hofmann, José María Martell, Svitlana Mayboroda

Research output: Contribution to journalArticlepeer-review

11 Scopus citations

Abstract

Let E ⊂ℝn+1, n= ≥ 2, be a closed, Ahlfors-David regular set of dimension n satisfying the "Riesz Transform bound" supℰ>0∫E|∫{y∈E:|x-y|>e}x - y/|x - y|n+1 f(y) dHn(y)|2dHn(x) ≤ C∫E|f|2 dHn.Assume further that E is the boundary of a domain ω ⊂ℝn+1 satisfying the Harnack Chain condition plus an interior (but not exterior) corkscrew condition. Then E is uniformly rectifiable.

Original languageEnglish (US)
Pages (from-to)2702-2729
Number of pages28
JournalInternational Mathematics Research Notices
Volume2014
Issue number10
DOIs
StatePublished - Jan 1 2014

Fingerprint Dive into the research topics of 'Uniform Rectifiability and Harmonic Measure III: Riesz Transform Bounds Imply Uniform Rectifiability of Boundaries of 1-sided NTA Domains'. Together they form a unique fingerprint.

Cite this