Beyond Besov Spaces, Part 2: Oscillation Spaces

摘要

We study several extensions of Besov spaces; these extensions include the oscillation spaces Op s,s’which take into account correlations between the positions of large wavelet coefficients through the scales and, more generally, spaces defined through the distributions of suprema of wavelet coefficients on wavelet subtrees. These spaces are independent of the particular wavelet basis chosen. Examples of applications will be taken from image processing and multifractal analysis.