Sublaplace和Subelliptic算子的整体Poincaré不等式

Global PoincaréInequalities for Sublaplacians and Other Subelliptic Operators

设f是Heisenberg型群N上局部Sobolev空间W_(loc)^(1,p)(N)中的函数,并且其次椭圆梯度L^P整体可积.本文证明了f在N上存在整体Poincaré不等式.对于Grush算子L=Δ_x+(α+1)~2|x|^(2α)Δ_y(α>0),也得到类似的结论.

Let f be in the localized Sobolev space Wloc ^q,p（N） on the Heisenberg type group N. Suppose that the subelliptic gradient is globally Lp integrable. We prove a Poincaré inequality for f on the entire space N. We also show analogous results for Grushin operators like L=△x＋（α＋1）2｜x｜2α △Ay（α〉0）.