Quasi-convex Functions in Carnot Groups  

作　　者：Mingbao SUN Xiaoping YANG 

机构地区：[1]Department of Applied Mathematics, Hunan Institute of Science and Technology, Yueyang 414000, Hu nan, China [2]Department of Applied Mathematics, Nanjing University of Science and Technology, Nanjing 210094, China [3]Department of Applied Mathematics, Nanjing University of Science and Technology, Nanjing 210094, China

出　　处：《Chinese Annals of Mathematics,Series B》2007年第2期235-242,共8页数学年刊（B辑英文版）

基　　金：Project supported by the Science Foundation for Pure Research of Natural Sciences of the Education Department of Hunan Province (No. 2004c251);the Hunan Provincial Natural Science Foundation of China (No. 05JJ30006);the National Natural Science Foundation of China (No. 10471063).

摘　　要：In this paper, the authors introduce the concept of h-quasiconvex functions on Carnot groups G. It is shown that the notions of h-quasiconvex functions and h-convex sets are equivalent and the L^∞ estimates of first derivatives of h-quasiconvex functions are given. For a Carnot group G of step two, it is proved that h-quasiconvex functions are locally bounded from above. Furthermore, the authors obtain that h-convex functions are locally Lipschitz continuous and that an h-convex function is twice differentiable almost everywhere.

关 键 词：h-Quasiconvex function Carnot group Lipschitz continuity 

分 类 号：O152[理学—数学]