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Hölder exponents at given points and wavelet coefficients. (Exposants de Hölder en des points donnés et coefficients d’ondelettes.) (French) Zbl 0665.42012

We prove that, for any \(\epsilon >0\) and any \(f\in C^{\epsilon}({\mathbb{R}}^ n)\), the Hölder exponent of f at a given point \(x_ 0\) can be explicitly computed, up to a logarithmic factor, by size conditions on the wavelet coefficients of f.

MSC:

42A38 Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type
42C40 Nontrigonometric harmonic analysis involving wavelets and other special systems
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