Caamaño Aldemunde, IvánJaramillo Aguado, Jesús ÁngelPrieto Yerro, M. ÁngelesRuiz de Alarcón, Alberto2023-06-172023-06-172020-11-091578-730310.1007/s13398-020-00959-4https://hdl.handle.net/20.500.14352/7599We 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.engjournal articlehttps//doi.org/10.1007/s13398-020-00959-4https://link.springer.com/article/10.1007%2Fs13398-020-00959-4open access517.982.2517.983Sobolev spacesVector-valued functionsEspacios de SobolevFunciones vectorialesMatemáticas (Matemáticas)Análisis matemático12 Matemáticas1202 Análisis y Análisis Funcional