  In this paper, we investigate the $W^{s,p}$-boundedness for stationary wave
operators of the Schr\"odinger operator with inverse-square potential
$$\mathcal L_a=-\Delta+\tfrac{a}{|x|^2}, \quad a\geq -\tfrac{(d-2)^2}{4},$$ in
dimension $d\geq 2$. We construct the stationary wave operators in terms of
integrals of Bessel functions and spherical harmonics, and prove that they are
$W^{s,p}$-bounded for certain $p$ and $s$ which depend on $a$. As corollaries,
we solve some open problems associated with the operator $\mathcal L_a$, which
include the dispersive estimates and the local smoothing estimates in dimension
$d\geq 2$. We also generalize some known results such as the uniform Sobolev
inequalities, the equivalence of Sobolev norms and the Mikhlin multiplier
theorem, to a larger range of indices. These results are important in the
description of linear and nonlinear dynamics for dispersive equations with
inverse-square potential.
