Advanced topology on the multiscale sequence spaces S

We pursue the study of the multiscale spaces Sν introduced by Jaffard in the context of multifractal analysis. We give the necessary and sufficient condition for Sν to be locally p-convex, and exhibit a sequence of p-norms that defines its natural topology. The strong topological dual of Sν is identified to another sequence space depending on ν, endowed with an inductive limit topology. As a particular case, we describe the dual of a countable intersection of Besov spaces.