# 3 mars 2020: 1 événement

### Mardi 3 mars 13:45-15:00 - Alexandros Eskenazis - Institut de Mathématiques de Jussieu-Sorbonne Université et Trinity College Cambridge

Discrete Littlewood-Paley-Stein theory and Pisier’s inequality for superreflexive targets

Résumé : In modern terminology, Enflo’s conjecture (1978) asserts that a Banach space $X$ has Rademacher type $p$ if and only if $X$ satisfies a metric property called Enflo type $p$. Loosely speaking, the conjecture suggests that all $X$-valued functions on the Hamming cube satisfy a dimension independent $L_p$ Poincaré inequality if and only if the same inequality holds merely for linear functions. In his 1986 work, Pisier showed that Banach spaces of Rademacher type $p$ have Enflo type $q$ for every $q<p$ and proved the endpoint Enflo type $p$ inequality with an additional logarithmic factor in the dimension of the Hamming cube. In this talk, I shall present joint work in progress with A. Naor, in which we improve Pisier’s bound for Banach spaces which admit an equivalent uniformly convex norm. The proof relies on (either new or recently proven) vector valued Littlewood-Paley-Stein theory on the Hamming cube.

En savoir plus : Séminaire d’Analyse Fonctionnelle