Some Properties of Quasiconvex Functions on the Heisenberg Group  

作　　者：Ming-bao Sun Xiao-ping Yang 

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

出　　处：《Acta Mathematicae Applicatae Sinica》2005年第4期571-580,共10页应用数学学报（英文版）

基　　金：Supportecl in part by SF for Pure Research of Natural Sciences of the Education Department of Hunan Province （No.2004c251）, Natural Science Foundation of Hunan Province （No.05JJ30006） and National Natural Science Foundation of China （No.10471063） and specialized Research Fund for Doctoral Program of Higher Education of China.

摘　　要：For the Heisenberg group, we introduce the concept of h-quasiconvex functions. We prove that the notions of h-quasiconvex functions and h-convex set are equivalent and that h-quasiconvex functions are locally bounded from above, and furthermore derive that h-convex functions are locally bounded, therefore it is locally Lipschitz continuous by using recent results by Danielli-Garofalo-Nhieu. Finally we give estimates of the L^∞ norm of the first derivatives of h-quasiconvex functions.For the Heisenberg group, we introduce the concept of h-quasiconvex functions. We prove that the notions of h-quasiconvex functions and h-convex set are equivalent and that h-quasiconvex functions are locally bounded from above, and furthermore derive that h-convex functions are locally bounded, therefore it is locally Lipschitz continuous by using recent results by Danielli-Garofalo-Nhieu. Finally we give estimates of the L^∞ norm of the first derivatives of h-quasiconvex functions.

关 键 词：h-quasiconvex function h-convex function Heisenberg group 

分 类 号：O174.13[理学—数学]