L^p-norm inequality using q-moment and its applications

Tomohiro Nishiyama

No 7yzvj, OSF Preprints from Center for Open Science

Abstract: For a measurable function on a set which has a finite measure, an inequality holds between two Lp-norms. In this paper, we show similar inequalities for the Euclidean space and the Lebesgue measure by using a q-moment which is a moment of an escort distribution. As applications of these inequalities, we first derive upper bounds for the Renyi and the Tsallis entropies with given q-moment and derive an inequality between two Renyi entropies. Second, we derive an upper bound for the probability of a subset in the Euclidean space with given Lp-norm on the same set.

Date: 2019-01-30
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Persistent link: https://EconPapers.repec.org/RePEc:osf:osfxxx:7yzvj

DOI: 10.31219/osf.io/7yzvj

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