Advanced topology on the multiscale sequence spaces S^ν

Abstract

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

30 pages, 2 figures. To appear in J. Math. Anal. Appl