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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, Center for Open Science.
    • Handle: RePEc:osf:osfxxx:7yzvj
    DOI: 10.31219/osf.io/7yzvj
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    References listed on IDEAS

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    1. Nishiyama, Tomohiro, 2018. "Improved Chebyshev inequality: new probability bounds with known supremum of PDF," OSF Preprints h9zfn, Center for Open Science.
    2. Tsallis, Constantino & Mendes, RenioS. & Plastino, A.R., 1998. "The role of constraints within generalized nonextensive statistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 261(3), pages 534-554.
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