Sobolev-Kantorovich inequalities under $CD(0, \infty)$ condition

V. I. Bogachev; A. V. Shaposhnikov; F. -Yu. Wang

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arXiv · 1603.07378

Sobolev-Kantorovich inequalities under $CD(0, \infty)$ condition

V. I. Bogachev·A. V. Shaposhnikov·F. -Yu. Wang

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Abstract

We refine and generalize several interpolation inequalities bounding the $L^p$ norm of a probability density with respect to the reference measure $\mu$ by its Sobolev norm and the Kantorovich distance to $\mu$ on a smooth weighted Riemannian manifold satisfying $CD(0, \infty)$ condition.

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BibTeX RIS

V. I. Bogachev, A. V. Shaposhnikov, F. -Yu. Wang. 2016-03-23. Sobolev-Kantorovich inequalities under $CD(0, \infty)$ condition. https://arxiv.org/abs/1603.07378

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