Abstract
We consider the Bochner-Riesz multiplier
\[
T
δ
f
^
(
ξ
)
=
(
1
−
|
ξ
|
2
)
δ
+
f
^
(
ξ
)
,
δ
>
0
,
\widehat {{T_\delta }f}(\xi ) = {(1 - {\left | \xi \right |^2})^\delta } + \hat f(\xi ),\qquad \delta > 0,
\]
where
^
\widehat {}
denotes the Fourier transform. It is shown that the multiplier operator
T
δ
{T_\delta }
is weak type
(
p
0
,
p
0
)
({p_0},\,{p_0})
acting on
L
p
0
(
R
n
)
{L^{p0}}({{\mathbf {R}}^n})
radial functions, where
p
0
{p_0}
is the critical value
2
n
/
(
n
+
1
+
2
δ
)
2n/(n + 1 + 2\delta )
.