Real interpolation of Sobolev spaces

Abstract

We prove that $W_p^1$ is an interpolation space between $W_{p_1}^1$ and $W_{p_2}^1$ for $p>q_0$ and $1\le p_1<p<p_2\le \infty$ on some classes of manifolds and general metric spaces, where $q_0$ depends on our hypotheses.

30 pages