We furnish conditions on the functions
p
(
t
)
,
f
(
t
)
p(t),f(t)
, and
g
(
t
)
g(t)
that are sufficient for the validity of the inequality,
α
2
δ
≥
γ
2
β
{\alpha ^2}\delta \geq {\gamma ^2}\beta
, in which
α
,
β
,
γ
\alpha ,\beta ,\gamma
, and
δ
\delta
respectively, are the integrals over a measurable set
E
E
of
p
(
t
)
g
(
t
)
,
p
(
t
)
g
2
(
t
)
,
p
(
t
)
f
(
t
)
p(t)g(t),p(t){g^2}(t),p(t)f(t)
, and
p
(
t
)
f
2
(
t
)
p(t){f^2}(t)
.