Characterizing Sobolev spaces of vector-valued functions

We are concerned here with Sobolev-type spaces of vector-valued functions. For an open subset Ω⊂RN and a Banach space V, we characterize the functions in Sobolev-Reshetnyak R1,p(Ω,V), where 1≤p≤∞, terms existence partial metric derivatives or w⁎-derivatives suitable integrability properties. In case p=∞ R1,∞(Ω,V) is characterized uniform local Lipschitz property. also consider special V=ℓ∞.