逐点反霍尔德不规则性的小波技术
Wavelets techniques for pointwise anti-Holderian irregularity
摘要：
本文从点态反Holder正则性的定义出发，引入了弱点态Holder正则性的概念。利用这一概念，可以像通常的逐点Holder正则性那样定义一个弱奇异谱。我们构造了一类满足多重分形形式的小波级数，从而证明了其上界的最优性。我们还证明了弱奇异谱与偶然奇异谱（这里记为强奇异谱）是不连通的，这是通过展示一个由弱奇异谱与强奇异谱不同的Davenport级数构成的多重分形函数来实现的.
英文摘要：
In this paper, we introduce a notion of weak pointwise Holder regularity, starting from the de nition of the pointwise anti-Holder irregularity. Using this concept, a weak spectrum of singularities can be de ned as for the usual pointwise Holder regularity. We build a class of wavelet series satisfying the multifractal formalism and thus show the optimality of the upper bound. We also show that the weak spectrum of singularities is disconnected from the casual one (denoted here strong spectrum of singularities) by exhibiting a multifractal function made of Davenport series whose weak spectrum di ers from the strong one.
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