Massive Laplacian isomorphism on Sobolev spaces
= Massive Laplacian isomorphism on Sobolev spaces
For every real $s$,
$$
-\Delta+1:H^{s+2}(\mathbb R^n)\to H^s(\mathbb R^n)
$$
is an isomorphism. Its inverse is the Fourier multiplier $(1+|\xi|^2)^{-1}$.