Characterizing Sobolev spaces of vector-valued functions

We are concerned here with Sobolev-type spaces of vector-valued functions. For an open subset Omega subset of R-N and a Banach space V, we characterize the functions in the Sobolev-Reshetnyak space R-1,R-p (Omega, V), where 1 <= p <= infinity, in terms of the existence of partial metric derivatives or partial w*-derivatives with suitable integrability properties. In the case p = infinity the Sobolev-Reshetnyak space R-1,R-infinity (Omega, V) is characterized in terms of a uniform local Lipschitz property. We also consider the special case of the space V = l(infinity). (C) 2022 The Authors. Published by Elsevier Inc.