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 $\mathrm{\text{CD}}(0,\infty )$ condition.

中文翻译：

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CD(0,∞) 条件下的 Sobolev–Kantorovich 不等式

我们细化和概括了几个插值不等式${\mathrm{大号}}^p$关于参考测度的概率密度范数$\mu$由其 Sobolev 范数和 Kantorovich 距离$\mu$在满足的光滑加权黎曼流形上$\mathrm{\text{光盘}}(0,\infty )$健康）状况。