论文标题
Sobolev将常数嵌入谎言组
The Sobolev embedding constant on Lie groups
论文作者
论文摘要
在本文中，我们估计了sobolev嵌入常规的属于非伴随的谎言基团，该subiemannian不均匀的Sobolev空间赋予了左不变测度。我们获得的界限仅取决于组及其次摩nannian结构，从而减少了最著名的对经典不均匀的sobolev嵌入常数$ \ mathbb {r}^d $的界限。作为应用程序，我们证明了本地和全球Moser-Trudinger的不平等现象。
In this paper we estimate the Sobolev embedding constant on general noncompact Lie groups, for sub-Riemannian inhomogeneous Sobolev spaces endowed with a left invariant measure. The bound that we obtain, up to a constant depending only on the group and its sub-Riemannian structure, reduces to the best known bound for the classical inhomogeneous Sobolev embedding constant on $\mathbb{R}^d$. As an application, we prove local and global Moser--Trudinger inequalities.
