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1 September 2016 Uniform rectifiability, Carleson measure estimates, and approximation of harmonic functions
Steve Hofmann, José María Martell, Svitlana Mayboroda
Duke Math. J. 165(12): 2331-2389 (1 September 2016). DOI: 10.1215/00127094-3477128

Abstract

Let ERn+1, n2, be a uniformly rectifiable set of dimension n. Then bounded harmonic functions in Ω:=Rn+1E satisfy Carleson measure estimates and are ε-approximable. Our results may be viewed as generalized versions of the classical F. and M. Riesz theorem, since the estimates that we prove are equivalent, in more topologically friendly settings, to quantitative mutual absolute continuity of harmonic measure and surface measure.

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Steve Hofmann. José María Martell. Svitlana Mayboroda. "Uniform rectifiability, Carleson measure estimates, and approximation of harmonic functions." Duke Math. J. 165 (12) 2331 - 2389, 1 September 2016. https://doi.org/10.1215/00127094-3477128

Information

Received: 6 August 2014; Revised: 2 July 2015; Published: 1 September 2016
First available in Project Euclid: 6 September 2016

zbMATH: 1359.28005
MathSciNet: MR3544283
Digital Object Identifier: 10.1215/00127094-3477128

Subjects:
Primary: 28A75
Secondary: 28A78, 31B05, 35J25, 42B20, 42B25, 42B37

Rights: Copyright © 2016 Duke University Press

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Vol.165 • No. 12 • 1 September 2016
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