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arXiv · 2007.14149

Reverse H\"{o}lder Inequalities for log-Lipschitz Functions

Emanuel Milman
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Abstract

Reverse H\"{o}lder 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 H\"{o}lder 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 Poincar\'e inequality.

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Emanuel Milman. 2020-07-28. Reverse H\"{o}lder Inequalities for log-Lipschitz Functions. https://arxiv.org/abs/2007.14149

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