Geodesic
The Young inequality and the ${\mit \Delta }_2$-condition
Philippe Laurençot1
1 Mathématiques pour l'Industrie et la Physique CNRS UMR 5640 Université Paul Sabatier–Toulouse 3 118 route de Narbonne F-31062 Toulouse Cedex 4, France
Colloquium Mathematicum, Tome 94 (2002) no. 2, pp. 221-223.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

If $\varphi : [0,\infty )\to [0,\infty )$ is a convex function with $\varphi (0)=0$ and conjugate function $\varphi ^*$, the inequality $xy \le \varepsilon \varphi (x) + C_\varepsilon \ \varphi ^*(y)$ is shown to hold true for every $\varepsilon \in (0,\infty )$ if and only if $\varphi ^*$ satisfies the ${\mit \Delta }_2$-condition.
DOI : 10.4064/cm94-2-4
Keywords: varphi infty infty convex function varphi conjugate function varphi * inequality varepsilon varphi varepsilon varphi * shown every varepsilon infty only varphi * satisfies mit delta condition

Philippe Laurençot 1

1 Mathématiques pour l'Industrie et la Physique CNRS UMR 5640 Université Paul Sabatier–Toulouse 3 118 route de Narbonne F-31062 Toulouse Cedex 4, France 
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Philippe Laurençot. The Young inequality and the ${\mit \Delta }_2$-condition. Colloquium Mathematicum, Tome 94 (2002) no. 2, pp. 221-223. doi : 10.4064/cm94-2-4. http://geodesic.mathdoc.fr/articles/10.4064/cm94-2-4/

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