Rectifiability of measures and the $eta_p$ coefficients
Rectifiability of measures and the $eta_p$ coefficients
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措施的可修正性和 $eta_p$ 系数
DOI：
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发表时间：
2017
期刊：
影响因子：
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通讯作者：
X. Tolsa
中科院分区：
文献类型：
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作者：
X. Tolsa
在Azzam和Tolsa以前的一些工作中，证明了n$-可求正性可以用涉及David-Semmes的平方函数来表征。η 2系数。在本文中，我们构造了一些反例，这些反例表明类似的特征对$eta_p$系数与$p
eq2$.这是在强烈对比的情况下发生的均匀$n$-可整流性。在本文的第二部分中，我们提供了一个替代的论点，最近的结果Edelen，Naber和Valtorta关于$n$-可求直的措施，有界低$n$维密度。我们的另一种证明来自于上述阿扎姆和托尔萨的作品之一中的电晕分解的轻微变化以及适当的近似参数。
In some former works of Azzam and Tolsa it was shown that $n$-rectifiability can be characterized in terms of a square function involving the David-Semmes $eta_2$ coefficients. In the present paper we construct some counterexamples which show that a similar characterization does not hold for the $eta_p$ coefficients with $p
eq2$. This is in strong contrast with what happens in the case of uniform $n$-rectifiability. In the second part of this paper we provide an alternative argument for a recent result of Edelen, Naber and Valtorta about the $n$-rectifiability of measures with bounded lower $n$-dimensional density. Our alternative proof follows from a slight variant of the corona decomposition in one of the aforementioned works of Azzam and Tolsa and a suitable approximation argument.