Caamaño Aldemunde, IvánJaramillo Aguado, Jesús ÁngelPrieto Yerro, M. Ángeles2023-06-222023-06-2220220022-247X10.1016/j.jmaa.2022.126250https://hdl.handle.net/20.500.14352/71429CRUE-CSIC (Acuerdos Transformativos 2022)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 the Sobolev-Reshetnyak space R1,p(Ω, V), where 1 ≤p≤∞, in terms of the existence of partial metric derivatives or partial w∗-derivatives with suitable integrability properties. In the case p=∞ the Sobolev-Reshetnyak space R1,∞(Ω, V)is characterized in terms of a uniform local Lipschitz property. We also consider the special case of the space V=l∞.engAtribución-NoComercial-SinDerivadas 3.0 Españahttps://creativecommons.org/licenses/by-nc-nd/3.0/es/journal articlehttps://doi.org/10.1016/j.jmaa.2022.126250https://www.sciencedirect.com/science/article/pii/S0022247X22002645open access517.982.2517.983Sobolev spacesVector-valued functionsAnálisis funcional y teoría de operadores