Representations of the spaces $C^∞(ℝ^N) ∩ H^{k,p}(ℝ^N)$
Volume 142 / 2000
Studia Mathematica 142 (2000), 135-148
DOI: 10.4064/sm-142-2-135-148
Abstract
We give a representation of the spaces $C^∞(ℝ^N) ∩ H^{k,p}(ℝ^N)$ as spaces of vector-valued sequences and use it to investigate their topological properties and isomorphic classification. In particular, it is proved that $C^∞(ℝ^N) ∩ H^{k,2}(ℝ^N)$ is isomorphic to the sequence space $s^{ℕ} ∩ l^2(l^2)$, thereby showing that the isomorphy class does not depend on the dimension N if p=2.
