On an extension of the Blaschke-Santalo inequality

Abstract

Let $K$ be a convex body and $K^{\circ }$ its polar body. Call $\varphi (K)=\frac{1}{|K||K^{\circ }|}{\int }_K{\int }_{K^{\circ }}<x,y{>}^{2}dxdy$. It is conjectured that $\varphi (K)$ 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 pages