We give a representation of the spaces $C^\infty(\R^N)\cap H^{k,p}(\R^N)$ as spaces of vector-valued sequences and use it to investigate their topological properties and isomorphic classification. In particular, it is proved that $C^\infty(\R^N)\cap H^{k,2}(\R^N)$ is isomorphic to the sequence space $s^\N\cal \ell^2(\ell^2)$, thereby showing that the isomorphy class does not depend on the dimension $N$ if $p=2$.
Representations of the spaces $C^infty(\R^N)cap H^{k,p}(\R^N)$
ALBANESE, Angela Anna;MOSCATELLI, Vincenzo
2000-01-01
Abstract
We give a representation of the spaces $C^\infty(\R^N)\cap H^{k,p}(\R^N)$ as spaces of vector-valued sequences and use it to investigate their topological properties and isomorphic classification. In particular, it is proved that $C^\infty(\R^N)\cap H^{k,2}(\R^N)$ is isomorphic to the sequence space $s^\N\cal \ell^2(\ell^2)$, thereby showing that the isomorphy class does not depend on the dimension $N$ if $p=2$.File in questo prodotto:
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