JournalspmVol. 75, No. 1pp. 1–10

On minimal Hölder gaps and Shannon entropy balance

  • Immanuel M. Bomze

    Universität Wien, Austria
On minimal Hölder gaps and Shannon entropy balance cover
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Abstract

When estimating a bilinear form in xx and yy by a product of two terms depending solely on xx or yy, the well known Hölder inequality which uses the product of a pp-norm and its dual comes easily into play. However, if one can choose pp freely, one could reduce this Hölder gap accordingly. This note addresses this elementary but apparently not too popular issue by using strict log-convexity of the pp-norm in 1p\frac 1p (sometimes called Littlewood's inequality). The optimal pp is characterized by a balance condition on the Shannon entropies of distributions related to xx and yy.

Cite this article

Immanuel M. Bomze, On minimal Hölder gaps and Shannon entropy balance. Port. Math. 75 (2018), no. 1, pp. 1–10

DOI 10.4171/PM/2009