论文标题
CD（0，N）空间中的加权Sobolev不平等
Weighted Sobolev Inequalities in CD(0,N) spaces
论文作者
论文摘要
在本说明中，我们证明了满足合适生长条件的非紧凑型CD（0，n）空间上的全球加权Sobolev不平等现象，该空间延伸到可能的非平滑和非Riemannian结构。我们在RCD（0，N）空间的背景下使用此结果，通过加权NASH不等式获得相应加权热内核的均匀界限。
In this note, we prove global weighted Sobolev inequalities on non-compact CD(0,N) spaces satisfying a suitable growth condition, extending to possibly non-smooth and non-Riemannian structures a previous result by V. Minerbe stated for Riemannian manifolds with non-negative Ricci curvature. We use this result in the context of RCD(0,N) spaces to get a uniform bound of the corresponding weighted heat kernel via a weighted Nash inequality.
