论文标题
log-lipschitz功能的反向Hölder不平等现象
Reverse Hölder Inequalities for log-Lipschitz Functions
论文作者
论文摘要
在概率空间上的一类功能的反向Hölder不等式构成了概率分析的重要工具。在重新审视了（修改的）log-sobolev不等式如何用于得出对数lipschitz函数类别的反向Hölder不平等，我们使用一般的传输 - entropy不平等获得了较弱的条件，这也可以处理大约处理log-lipschitz函数。条件以最弱的形式退化为满足浓度不平等的假设。我们将其与一个基础空间只能满足庞加莱不平等的情况进行比较。
Reverse Hölder inequalities for a class of functions on a probability space constitute an important tool in Analysis in Probability. After revisiting how a (modified) log-Sobolev inequality can be used to derive reverse Hölder inequalities for the class of log-Lipschitz functions, we obtain a weaker condition using general Transport-Entropy inequalities, which can also handle approximately log-Lipschitz functions. In its weakest form, the condition degenerates to the assumption of satisfying a concentration inequality. We compare this with a scenario in which the underlying space only satisfies a Poincaré inequality.
