Sharpening the gap between $L^1$ and $L^2$ norms

Paata Ivanisvili, Yonathan Stone

We refine the classical Cauchy--Schwartz inequality $\Vert X{\Vert }_1\le \Vert X{\Vert }_2$ by demonstrating that for any $p$ and $q$ with $q>p>2$, there exists a constant $C=C(p,q)$ such that…