C. Fefferman has shown that the disc multiplier is not bounded on
L
p
(
R
n
)
,
n
>
1
,
p
≠
2
{L^p}({{\mathbf {R}}^n}),n > 1,p \ne 2
. In contrast, C. Herz showed that, when restricted to
L
p
{L^p}
radial functions, it is bounded on
L
p
(
R
n
)
{L^p}({{\mathbf {R}}^n})
if and only if
2
n
/
(
n
+
1
)
>
p
>
2
n
/
(
n
−
1
)
2n/(n + 1) > p > 2n/(n - 1)
. We show that it is not weakly bounded for
p
=
2
n
/
(
n
+
1
)
p = 2n/(n + 1)
or
p
=
2
n
/
(
n
−
1
)
p = 2n/(n - 1)
.