Advanced topology on the multiscale sequence spaces S-nu

We put-sue the Study of the multiscale spaces S-v introduced by Jaffard in the context of multifractal analysis. We give the necessary and Sufficient condition for S-v to be locally p-convex, and exhibit a sequence of p-norms that defines its natural topology. The strong topological dual of S-v is identified to another sequence space depending on v, endowed with an inductive limit topology. As a particular case, we describe the dual of a countable intersection of Besov spaces. (C) 2007 Elsevier Inc. All rights reserved.