Let $u \in H^{\frac 12}(M)$ on a compact closed Riemannian manifold. Can someone refer me to a source where the inequality $$\lVert u - \bar u \rVert_{L^{2^*}} \leq C|u|_{H^{\frac 12}}$$ is proved, or something similar involving the fractional RHS? Here $2^*$ is the usual conjugate and $\bar u$ is the mean value of $u$.
Thanks
