suppose I have three functions, f(x), g(x) and h(x). I want to know if there are any bounds on the integrals of these quantities. Specifically if I can measure a and b where \begin{equation} \int_{0}^{\infty}|f(x)g^*(x)|^2dx=a \end{equation} and \begin{equation} \int_{0}^{\infty}|f(x)h^*(x)|^2dx=b \end{equation} Is there an upper bound on c where c is defined below? \begin{equation} \int_{0}^{\infty}|h(x)g^*(x)|^2dx=c \end{equation}
Thanks!