Noncommutative Khintchine inequalities in interpolates of L_p-spaces

Abstract:

The Khintchine inequalities first appeared as a result about Rademacher variables in probability theory and have been the object of a rich literature due, in particular, to their central role in harmonic analysis. Their introduction in the noncommutative setting is due to Lust-Piquard in 1986. They were then vastly studied, usually to answer one or both of the following questions. In which spaces do they hold ? And for which random variables ? In this talk, we will do a short survey on Khintchine inequalities and briefly introduce noncommutative harmonic analysis. We present new results in this context, Khintchine inequalities hold in weak L1, they can also be expressed in a unified way for all interpolates of Lp-spaces.