التفاصيل البيبلوغرافية
| العنوان: |
Uniform rectifiability from Carleson measure estimates and $\varepsilon$-approximability of bounded harmonic functions |
| المؤلفون: |
Garnett, John, Mourgoglou, Mihalis, Tolsa, Xavier |
| المصدر: |
Duke Math. J. 167, no. 8 (2018), 1473-1524 |
| سنة النشر: |
2016 |
| المجموعة: |
Mathematics |
| مصطلحات موضوعية: |
Mathematics - Classical Analysis and ODEs, Mathematics - Analysis of PDEs, 31A15, 28A75, 28A78 |
| الوصف: |
Let $\Omega\subset\mathbb R^{n+1}$, $n\geq1$, be a corkscrew domain with Ahlfors-David regular boundary. In this paper we prove that $\partial\Omega$ is uniformly $n$-rectifiable if every bounded harmonic function on $\Omega$ is $\varepsilon$-approximable or if every bounded harmonic function on $\Omega$ satisfies a suitable square-function Carleson measure estimate. In particular, this applies to the case when $\Omega=\mathbb R^{n+1}\setminus E$ and $E$ is Ahlfors-David regular. Our results solve a conjecture posed by Hofmann, Martell, and Mayboroda in a recent work where they proved the converse statements. Here we also obtain two additional criteria for uniform rectifiability. One is given in terms of the so-called "$SComment: Correction of a few typos and general reorganization of the arguments. Additional references |
| نوع الوثيقة: |
Working Paper |
| DOI: |
10.1215/00127094-2017-0057 |
| URL الوصول: |
http://arxiv.org/abs/1611.00264 |
| رقم الانضمام: |
edsarx.1611.00264 |
| قاعدة البيانات: |
arXiv |