中文摘要：

本文研究了关于投影不等式的Petty猜想这个凸体理论中的一个著名公开问题．利用凸体的Lp—Brunn-Minkowski—Firey理论，建立了Petty投影不等式猜想的Lp-版本的几个不同精度的小等式，推广了已有文献的结论．

英文摘要：

In this article, we further study a famous open problem relating to Petty＇s con- jectured projection inequality in convex geometry. By using the Lp-Brunn-Minkowski-Firey theory of convex bodies, we establish a number of different precision inequalities relating to Lp-version of the Petty＇s conjectured projection inequality. Our results are some generalizations in the results of the previous literature.