Beyond Besov spaces - Part 1: Distributions of wavelet coefficients

We determine which information can be extracted from the distributions of the wavelet coefficients of a function f at each scale, but does not depend on the particular wavelet basis which is chosen. This information can be naturally expressed in terms of one increasing function v(f) (alpha), and the knowledge of this function yields strictly more information than the knowledge of the Besov spaces that contain f. Examples of use of this additional information will be taken from image processing and multifractal analysis.