In this paper, weak Poincaré inequalities are obtained for convolution probabilities with explicit rate functions by constructing suitable Lyapunov functions. Here, one of these Lyapunov functions is introduced for the first time and can be used to improve parts of results on the estimate of rate functions for super Poincaré inequalities 13 as well. In addition, these weak Poincaré inequalities are applied to some concrete examples, which can refine some of results even for the case without convolution.

中文翻译：

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卷积概率度量的弱庞加莱不等式

在本文中，通过构造合适的 Lyapunov 函数，获得了具有显式速率函数的卷积概率的弱 Poincaré 不等式。在这里，首次引入其中一个 Lyapunov 函数，可用于改进超庞加莱不等式的速率函数估计的部分结果13也是。此外，这些弱 Poincaré 不等式被应用到一些具体的例子中，即使对于没有卷积的情况也可以细化一些结果。