Quasi-convex Functions in Carnot Groups*
Mingbao Sun , Xiaoping Yang
Chinese Annals of Mathematics, Series B ›› 2007, Vol. 28 ›› Issue (2) : 235 -242.
Quasi-convex Functions in Carnot Groups*
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.
h-Quasiconvex function / Carnot group / Lipschitz continuity / 43A80 / 26B25
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