In this paper, we investigate the
W
s
,
p
W^{s,p}
-boundedness for stationary wave operators of the Schrödinger operator with inverse-square potential
L
a
=
−
Δ
+
a
|
x
|
2
,
a
≥
−
(
d
−
2
)
2
4
,
\begin{equation*} \mathcal L_a=-\Delta +\tfrac {a}{|x|^2}, \quad a\geq -\tfrac {(d-2)^2}{4}, \end{equation*}
in dimension
d
≥
2
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
W^{s,p}
-bounded for certain
p
p
and
s
s
which depend on
a
a
. As corollaries, we solve some open problems associated with the operator
L
a
\mathcal L_a
, which include the dispersive estimates and the local smoothing estimates in dimension
d
≥
2
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.