 Kahane-Khintchine inequality

For a Rademacher sum in a normed vector space, any two fixed positive moments of its norm are comparable with constants depending only on those moments. The sharp Rademacher second-moment inequality gives the sharp first-to-second moment comparison $\Vert S{\Vert }_{L^2}\le \sqrt{2}\Vert S{\Vert }_{L^1}$ for arbitrary coefficients.