Uniform Rectifiability, Carleson measure estimates, and approximation of harmonic functions
Uniform Rectifiability, Carleson measure estimates, and approximation of harmonic functions
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均匀可整流性、Carleson 测量估计以及谐波函数的近似
DOI：
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发表时间：
2014
期刊：
影响因子：
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通讯作者：
S. Mayboroda
中科院分区：
文献类型：
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作者：
S. Hofmann;J. M. Martell;S. Mayboroda
设E子集mathbb{R}^{n+1}$，$nge 2$是n维一致可求长集.则$Omega：= mathbb{R}^{n+1}集减E$中的有界调和函数满足Carleson测度估计，并且是“变分逼近”的.我们的结果可以看作是经典F.和M. Riesz定理，因为我们证明的估计是等价的，在更拓扑友好的设置，定量相互绝对连续的调和措施，表面措施。
Let $Esubset mathbb{R}^{n+1}$, $nge 2$, be a uniformly rectifiable set of dimension $n$. Then bounded harmonic functions in $Omega:= mathbb{R}^{n+1}setminus E$ satisfy Carleson measure estimates, and are "$varepsilon$-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.