The Lp Loomis–Whitney inequality

In this paper, we establish the LpLp Loomis–Whitney inequality for even isotropic measures in terms of the support function of LpLp projection bodies with complete equality conditions. This generalizes Ball's Loomis–Whitney inequality to the LpLp setting. In addition, the sharp upper bound of the minimal p  -mean width of LpLp zonoids is obtained.