Representations of the spaces C-infinity(R-N) boolean AND H-k,H-p(R-N)

We give a representation of the spaces C-infinity(R-N) boolean AND H-k,H-p( R-N) as spaces of vector-valued sequences and use it to investigate their t opological properties and isomorphic classification. In particular, it is p roved that C-infinity(R-N) boolean AND H-k,H-2(R-N) is isomorphic to the se quence space s(N) boolean AND l(2)(l(2)), thereby showing that the isomorph y class does not depend on the dimension N if p = 2.