Séminaires : Séminaire d'Analyse Fonctionnelle

Equipe(s) : af,
Responsables :E. Abakoumov - D. Cordero-Erausquin - G. Godefroy - O. Guédon - B. Maurey - G.Pisier
Email des responsables :
Salle : salle 13 - couloir 15-16 - 4ème étage
Adresse :Campus Pierre et Marie Curie
Le Jeudi à 10h30 -  IMJ-PRG - 4 place Jussieu - 75005 PARIS

Orateur(s) Alexander Volberg - Michigan,
Titre Poincaré inequalities on Hamming cube: analysis, combinatorics, probability
Horaire10:00 à 13:30
RésumeWe improve the constant $\frac\pi2$ in $L^1$-Poincar\'e inequality on Hamming cube. For Gaussian space the sharp constant in $L^1$ inequality is known, and it is $\sqrt\frac\pi2$ (Maurey--Pisier). For Hamming cube the sharp constant is not known, and $\sqrt\frac\pi2$ gives an estimate from below for this sharp constant. On the other hand, L. Ben Efraim and F. Lust-Piquard have shown an estimate from above: $C_1\le \frac\pi2$. Their proof was using non-commutative harmonic analysis., semi-groups in the space of matrices. There are at least two other proofs of the same estimate from above (we present one or two of them). Since those proofs are very different from the proof of Ben Efraim and Lust-Piquard but gave the same constant, that might have indicated that constant is sharp. But here we give a better estimate from above, showing that $C_1$ is strictly smaller than $\frac\pi2$. It is still not clear whether $C_1> \sqrt\frac\pi2$. We discuss this circle of questions including the possible role of the so-called curl space in combinatorics of calculation.
Sallesalle 13 - couloir 15-16 - 4ème étage
AdresseCampus Pierre et Marie Curie