Inequalities between $L^p$-norms for log-concave distributions

Tomohiro Nishiyama

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arXiv · 1903.10101

Inequalities between $L^p$-norms for log-concave distributions

Tomohiro Nishiyama

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Abstract

Log-concave distributions include some important distributions such as normal distribution, exponential distribution and so on. In this note, we show inequalities between two Lp-norms for log-concave distributions on the Euclidean space. These inequalities are the generalizations of the upper and lower bound of the differential entropy and are also interpreted as a kind of expansion of the inequality between two Lp-norms on the measurable set with finite measure.

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BibTeX RIS

Tomohiro Nishiyama. 2019-03-25. Inequalities between $L^p$-norms for log-concave distributions. https://arxiv.org/abs/1903.10101

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