 Hölder's inequality

For conjugate exponents $p,q\in [1,\infty ]$, Hölder's inequality states $\Vert fg{\Vert }_1\le \Vert f{\Vert }_p\Vert g{\Vert }_q$. For finite vectors, the case $p=1$, $q=\infty$ is $|x^{T}y|\le \Vert x{\Vert }_1\Vert y{\Vert }_{\infty }$.