Sobolev-Kantorovich inequalities under $CD(0, \infty)$ condition
Probability
2020-12-21 v3 Differential Geometry
Functional Analysis
Abstract
We refine and generalize several interpolation inequalities bounding the norm of a probability density with respect to the reference measure by its Sobolev norm and the Kantorovich distance to on a smooth weighted Riemannian manifold satisfying condition.
Keywords
Cite
@article{arxiv.1603.07378,
title = {Sobolev-Kantorovich inequalities under $CD(0, \infty)$ condition},
author = {V. I. Bogachev and A. V. Shaposhnikov and F. -Yu. Wang},
journal= {arXiv preprint arXiv:1603.07378},
year = {2020}
}