Beyond Besov spaces
by
Stéphane Jaffard
Université Paris XII and Institut Universitaire de France

We study three generalizations of Besov spaces: The Oscillation spaces Ossp, which take into account correlations between the positions of large wavelet coefficients through the scales, and give a natural extension of Besov spaces Besov to negative ps. The spaces BSP are a more direct extension of Besov spaces to negative ps. Finally, the spaces S^\mu, allows to retain the maximal information that can be extracted from the distributions of wavelet coefficients at each scale, but is independent of the particular wavelet basis chosen; it gives a function space setting to all models based on distributions of wavelet coefficients. We give examples of use of these spaces in several fields of applications, including multifractal analysis, the study of functions of bounded variations, and wavelet-based statistical models.

Date received: February 2, 2001

Copyright © 2001 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cafv-08.