Beyond Besov spaces. I: Distributions of wavelet coefficients
Wavelets are unconditional bases of Besov spaces \(B_p^{s,q}\), and the knowledge of Besov spaces to which a function \(f\) belongs can be deduced from the distribution of the wavelet coefficient of \(f\) at all scales. In the paper under review, the author considers the information that can be obtained from the distribution of wavelet coefficients at each scale, with independence of the wavelet. He shows that a convenient ``wavelet profile'', which is a function \(\nu_f(\alpha)\) that arises naturally in the multifractal analysis of random processes, gives more information than the knowledge of the Bessov spaces that contain \(f\). The results are tested by considering the wavelet profiles of some classical examples, such as Weierstrass functions and Brownian motions.
Besov spaces, multifractal formalism, oscillation spaces
scientific article; zbMATH DE number 2133422