2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/141180Let $K$ be a convex body and $K^\circ$ its polar body. Call $ϕ(K)=\frac{1}{|K||K^\circ|}\int_K\int_{K^\circ}< x,y>^2 dxdy$. It is conjectured that $ϕ(K)$ is maximum when $K$ is the euclidean ball. In particular this statement implies the Blaschke-Santalo inequality. We verify this conjecture when $K$ is restricted to be a $p$--ball.7 pagesFunctional Analysis52A20; 52A40; 46B20text