An inequality of the form (1.1) is established, where
p
,
q
p,q
are real-valued functions on an interval
[
a
,
b
)
[a,b)
of the real line, with
−
∞
>
a
>
b
>
∞
,
p
(
x
)
>
0
- \infty > a > b > \infty ,p(x) > 0
on
[
a
,
b
)
,
μ
0
[a,b),{\mu _0}
is a real number and
f
f
is a complex-valued function in a linear manifold so chosen that all three integrals in (1.1) are absolutely convergent. The problem is singular in that while
p
−
1
∈
L
(
a
,
b
)
{p^{ - 1}} \in L(a,b)
we require
q
q
to have a behavior at
b
b
of such a form that
q
∉
L
(
a
,
b
)
q \notin L(a,b)
.