Beyond Besov Spaces Part 1: Distributions of Wavelet Coefficients

Abstract

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 ν _f (α), 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.