Wavelets techniques for pointwise anti-Holderian irregularity

Details Wavelets techniques for pointwise anti-Holderian irregularity Wavelets techniques for pointwise anti-Holderian irregularity

2011-04-04

arxiv.org/abs/1104.0653v1

Constructive Approximation 33 (2011) 41-75

Mathematics

Functional Analysis

Scientific paper

10.1007/s00365-010-9120-9

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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