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

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  • Nishiyama, Tomohiro

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.

Suggested Citation

  • Nishiyama, Tomohiro, 2019. "L^p-norm inequality using q-moment and its applications," OSF Preprints 7yzvj_v1, Center for Open Science.
    • Handle: RePEc:osf:osfxxx:7yzvj_v1
    DOI: 10.31219/osf.io/7yzvj_v1
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