论文标题
Carnot组II中的极性坐标
Polar Coordinates in Carnot groups II
论文作者
论文摘要
如果Carnot集团携带同质规范，则可以两极分化，其功率是$ p $ -sub-sub-sub-laplacian运营商的基本解决方案。这些组还支持水平极坐标系统。我们证明相反的说明是正确的：如果Carnot组支持具有合适性能的水平极性坐标系，则它是可极化的。
A Carnot group is polarizable if it carries a homogeneous norm whose powers are fundamental solutions for the $p$-sub-Laplacian operators for all $1<p \le \infty$. Such groups also support a system of horizontal polar coordinates. We prove that the converse statement is true: if a Carnot group supports a horizontal polar coordinate system with suitable properties, then it is polarizable.
