On minimal Hölder gaps and Shannon entropy balance
- Author(s)
- Immanuel Bomze
- Abstract
When estimating a bilinear form in x and y by a product of two terms depending solely on x or y, the well known Hölder inequality which uses the product of a p-norm and its dual comes easily into play. However, if one can choose p 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 p-norm in 1/p (sometimes called Littlewood's inequality). The optimal p is characterized by a balance condition on the Shannon entropies of distributions related to x and y.
- Organisation(s)
- Department of Statistics and Operations Research, Research Network Data Science
- Journal
- Portugaliae Mathematica
- Volume
- 75
- Pages
- 1-10
- No. of pages
- 10
- ISSN
- 0032-5155
- DOI
- https://doi.org/10.4171/PM/2009
- Publication date
- 07-2018
- Peer reviewed
- Yes
- Austrian Fields of Science 2012
- 101015 Operations research
- Keywords
- ASJC Scopus subject areas
- Mathematics(all)
- Portal url
- https://ucris.univie.ac.at/portal/en/publications/on-minimal-hoelder-gaps-and-shannon-entropy-balance(06601b7b-e89f-487e-9cc6-6ec88dd13d86).html