Is $\Delta^{-1}$ a bounded operator?

Question

Is the inverse Laplacian $\Delta^{-1}: H^{m+2}(M)\mapsto H^m(M)|1$ a bounded operator? Where $M$ is a compact manifold and $H^m(M)|1$ means its elements $f \in H^m(M)$ and $\langle1,f\rangle=\int_{M}f dx=0$. Could anyone give me a rough proof, or give me some references. I can't find any reference which give a detailed proof of this. Thank you in advance.