# Discrete Sobolev Space and Sobolev Spaces of Banach Space valued functions

This is a reference request.
Can someone kindly give me some refernce(Books/papers) on

1. Discrete Sobolev Space (like we use Discrete $L^p$ spaces of $g\colon\Omega\to\Bbb R$ maps with norm given as summations );
2. Sobolev Spaces of Banach Space valued Maps a generalization of $\Bbb R^n$ valued maps).

$W^{m,p}$consisting of $f \colon\Omega\to X$ where $\Omega \subset \Bbb R^n$ and $X$ is a Banach space. In general $X$ can be thought of $\Bbb R^d$.

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