We explore upper bounds on Kantorovich transport distances between probability measures on the Euclidean spaces in terms of their Fourier-Stieltjes transforms, with focus on non-Euclidean metrics. The results are illustrated on empirical measures in the optimal matching problem on the real line.

中文翻译：

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非欧氏度量在欧氏空间上的传输不等式

我们根据傅立叶-Stieltjes变换探索欧几里得空间上概率度量之间的Kantorovich传输距离的上限，重点是非欧几里德度量。结果以实测最优匹配问题中的经验度量进行说明。