I have come across the following formula for the positive square root of the (negative) 3D Laplacian
$$(-\nabla^2)^{\frac{1}{2}}[u](y) = C \text{ p.v. }\int_{\mathbb{R}^3}\frac{u(y)-u(x)}{\|y-x\|^4}dx$$
as well as the one-sided inverse of this operator:
$$(-\nabla^2)^{-\frac{1}{2}}[u](y) = D\int_{\mathbb{R}^3}\frac{u(x)}{\|y-x\|^2}dx$$.
Are there analogous formulas for the operator $$(-\nabla^2 +m^2 )^{\frac{1}{2}}$$ where m is a real number?