论文标题
Carnot组中Sobolev和BV空间的通用热半群特征
A universal heat semigroup characterisation of Sobolev and BV spaces in Carnot groups
论文作者
论文摘要
通常，在河畔摩曼尼亚的几何形状中，通常没有已知的热核的明确表示，并且这些函数无法具有任何对称性。特别是，它们不是控制距离的函数，也不是在LIE代数的任何层中的球形对称。尽管有这些不利的方面，但在本文中，我们通过加热核的整体解耦属性，在Carnot组中对Sobolev和$ bv $空间进行了新的热半群特征。
In sub-Riemannian geometry there exist, in general, no known explicit representations of the heat kernels, and these functions fail to have any symmetry whatsoever. In particular, they are not a function of the control distance, nor they are for instance spherically symmetric in any of the layers of the Lie algebra. Despite these unfavourable aspects, in this paper we establish a new heat semigroup characterisation of the Sobolev and $BV$ spaces in a Carnot group by means of an integral decoupling property of the heat kernel.
