In
R
n
{{\mathbf {R}}^n}
define
(
T
λ
,
r
f
)
(
ξ
)
=
f
^
(
ξ
)
(
1
−
|
r
−
1
ξ
2
|
)
+
λ
({T_{\lambda ,r}}f)(\xi ) = \hat f(\xi )(1 - \left | {{r^{ - 1}}{\xi ^2}} \right |)_ + ^\lambda
. If
n
≥
3
n \geq 3
,
λ
>
1
2
(
n
−
1
)
/
(
n
+
1
)
\lambda > \tfrac {1}{2}(n - 1)/(n + 1)
and
2
≤
p
>
2
n
/
(
n
−
1
−
2
λ
)
2 \leq p > 2n/(n - 1 - 2\lambda )
, then
lim
r
→
∞
T
λ
,
r
f
(
x
)
=
f
(
x
)
{\lim _{r \to \infty }}{T_{\lambda ,r}}f(x) = f(x)
a.e. for all
f
∈
L
p
(
R
n
)
f \in {L^p}({{\mathbf {R}}^n})
.