非齐次随机圆盘型康托尔集的Favard长度
Favard length of non-homogeneous random disc-like Cantor sets
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中文总结 AI 辅助
本文研究了非齐次随机四角康托尔集的Favard长度衰减，给出了尖锐估计，证明了Mattila下界的尖锐性，并构造了正解析容量但零Favard长度的新例子。
中文摘要 AI 辅助
Favard长度是平面集的正交投影的平均长度。我们为Garnett在1970年代引入的非齐次四角康托尔集的随机变体的Favard长度衰减提供了尖锐估计。作为推论，我们获得了例子，表明Mattila关于Favard长度的经典下界（基于Riesz容量）在所有可能的衰减速率下都是尖锐的。我们还获得了一族新的具有正解析容量和零Favard长度的集合的例子。
英文摘要
The Favard length of a planar set is the average length of its orthogonal projections. We provide sharp estimates for the Favard length decay of a random variant of the non-homogeneous four corner Cantor sets introduced by Garnett in the 1970s. As a corollary, we obtain examples which show that Mattila's classical lower bound on the Favard length in terms of the Riesz capacity is sharp for all possible decay rates. We also obtain a new family of examples of sets with positive analytic capacity and zero Favard length.
