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Sobolev-Kantorovich inequalities under $CD(0, \infty)$ condition
V. I. Bogachev, A. V. Shaposhnikov, F. -Yu. Wang · 2016-03-24 · via math.PR updates on arXiv.org

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

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