Let $f$ be measurable and $f:(0,t) \to (0,\infty). $ The integral after using Tonelli's theorem looks like this: $\int_{[0,1]} \int_{[0,1]} ( \frac{f(x)}{f(y)} + \frac{f(y)}{f(x)})d(\lambda \times \lambda) = \int_{[0,1]} f(x)d\lambda(x) \int_{[0,1]} \frac{1}{f(y)}d\lambda(y) + \int_{[0,1]} \frac{1}{f(x)}d\lambda(x) \int_{[0,1]} f(y)d\lambda(y)$
Is there any way to estimate the values of these integrals?