中文摘要：

引入了第i个Lp-混合仿射表面积和Lp-极曲率像概念,建立了几个与新概念及Lp-质心体、p-Blaschke体有关的不等式,获得了关于Lp-混合仿射表面积的Blaschke-Santalo类不等式.所获结果能得到经典对偶Urysohn不等式的广义形式.

英文摘要：

In this paper, the concepts of the i th Lp-mixed affine surface area and Lp-polar curvature images are introduced, some new inequalities connecting these new notions with Lp-centroid bodies and p-Blaschke bodies are established. Moreover, a Blaschke-Santal6 type inequality for Lp-mixed affine surface area is established. Our results also imply a generalization of the class dual Urysohn inequalities.