Lp-质心体的反向包含关系与不等式

Reverse Inclusion Forms and Inequalities of L_p-Centroid Bodies

从Lp-质心体的一个包含关系式ΓKΓpKΓqKΓ∞K(1≤p≤q≤∞)入手,研究它的反向包含关系,得到:当1≤n≤p≤q≤∞时,(p-1)cnΓ∞K(p-1)ΓpK(q-1)ΓqK(q-1)cpΓK,其中cp,cn分别表示只与p,n有关的常数.进一步,用Lp-质心体的支撑函数估计了凸体截面体积的上下界.

The inclusion form of Lp-centroid bodies is introduced, and its reverse form discussed. An inclusion of the form （p - 1 ）cn Г∞ （p - 1） Гp KC （ q - 1 ）cp ГK is established, where 1 ≤n≤p≤q≤∞ and cp, cn are universal constants depending only on p, n respectively. Furthermore, boundness of the volume of the central section is estimated with the support function of Lp-centroid bodies.