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) .