泛Holder级集上箱维数的精确公式
Exact formula on upper box dimension of generic Hölder level sets
AI总结：
本文首次为一大类自相似集提供了泛Holder级集上箱维数的精确公式，证明其维数为dim_H F - α。
摘要：
在过去的几十年里，函数的级集大小在涉及不同正则性和尺寸概念的各种设置中已被广泛研究。在Holder函数的情况下，作者们提供了各种界，但截至目前为止，尚未发现任何研究维度的显式公式，且结果仅适用于非常特定的分形。在本文中，首次针对一大类自相似集，我们证明了对于这些分形，定义在F⊆R^p上的通用1-Hölder-α函数的Lebesgue几乎每一个级集的上箱维数为dim_H F - α。
英文摘要：
In the previous decades, the size of level sets of functions have been extensively studied in various setups involving different regularity properties and size notions. In the case of Hölder functions, the authors have provided various bounds, but to date no explicit formulae have been found for any studied dimension and the results were valid only about very specific fractals. In this paper, for the first time, we have a result valid for a large class of self-similar sets, namely we prove that for these fractals Lebesgue almost every level set of the generic 1-Hölder-$α$ function defined on $F\subseteq \mathbb{R}^p$ has upper box dimension $\dim_H F - α$.
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