In this paper we characterize the weights
w
,
v
w,v
for which
‖
S
ϕ
f
‖
p
,
w
≤
C
‖
f
‖
q
,
v
{\left \| {{S_\phi }f} \right \|_{p,w}} \leq C{\left \| f \right \|_{q,v}}
, for
f
f
nonincreasing, where
S
ϕ
f
=
∫
0
∞
ϕ
(
x
,
y
)
f
(
y
)
d
y
{S_\phi }f = \smallint _0^\infty {\phi (x,y)f(y)dy}
.