%0 Journal Article
%A Caamaño Aldemunde, Iván
%A Jaramillo Aguado, Jesús Ángel
%A Prieto Yerro, M. Ángeles
%A Ruiz de Alarcón, Alberto
%T Sobolev spaces of vector-valued functions
%D 2020
%@ 1578-7303
%U https://hdl.handle.net/20.500.14352/7599
%X We are concerned here with Sobolev-type spaces of vector-valued functions. For an open subset Ω ⊂ R N and a Banach space V , we compare the classical Sobolev space W1,p(Ω, V ) with the so-called Sobolev-Reshetnyak space R1,p(Ω, V ). We see that, in general, W1,p(Ω, V ) is a closed subspace of R1,p(Ω, V ). As a main result, we obtain that W1,p(Ω, V ) = R1,p(Ω, V ) if, and only if, the Banach space V has the Radon-Nikod´ym property.
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