2019/03/25 by Tomohiro Nishiyama, Nishiyama, Tomohiro
Mathematics · #Mathematical Inequalities and Applications #Mathematical Approximation and Integration #Mathematical Analysis and Transform Methods
paper · pdf · doi:10.48550/arxiv.1903.10101
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.