I have to show that $(1+\Delta)^s:H^k(U)\rightarrow H^{k-2s}(U)$ is an isomorphism where $\Delta$ is the Laplacian on $U\subset\mathbb{R}^n$ where $U$ has compact support and $H^k(U),H^{k-s}(U)$ are the Sobolov spaces.
I know that $(1+\Delta)^s$ is a differential operator of order $2s$, and hence it extends to a continuous function from $H^k(U)\rightarrow H^{k-2s}(U)$ for all $k\in \mathbb{Z}$. But I do not know what to go about the rest of the problem.
I would appreciate any help on this.