Mathematical Formula:

Hölder Inequality

The inequality $\|g\|_q \cdot \|f\|_p \geq \|g \cdot f\|_1$ is valid for any real numbers $p$ and $q$ with $p \gt 1$, $q \gt 1$, and $1 = \frac1p + 1/q$, where $\|f\|_p$ denotes the $L^p$-norm of $f$.