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| Quasi-convex Functions in Carnot Groups |
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Citation： |
Mingbao SUN,Xiaoping YANG.Quasi-convex Functions in Carnot Groups[J].Chinese Annals of Mathematics B,2007,28(2):235~242 |
| Page view： 1350
Net amount： 897 |
Authors： |
Mingbao SUN; Xiaoping YANG |
Foundation： |
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) and the National Natural Science Foundation of China (No. 10471063). |
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| Abstract： |
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^{\infty} 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. |
Keywords： |
h-Quasiconvex function, Carnot group, Lipschitz continuity |
Classification： |
43A80, 26B25 |
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