Reference to Lebesgue space on manifolds

Question

I am looking for a reference to the Lebesgue spaces $L^p(M)$, where $M$ is a Riemannian manifold. This question is motivated by $L^p(\partial\Omega)$ where $\partial\Omega$ is the boundary of a smooth bounded domain $\Omega \subset \mathbb{R}^n$. That is, $\partial\Omega$ is considered as a compact Riemannian submanifold of $\mathbb{R}^n$.