## 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

### Keywords:

Hölder exponent; wavelet coefficients