Noncommutative Khintchine inequalities in interpolation spaces of L p -spaces

International audienceWe prove noncommutative Khintchine inequalities for all interpolation spaces between L p and L 2 with p 2 and p < 2. It produces a new proof of Khintchine inequalities for p < 1 for free variables. To complete the picture, we exhibit counterexamples which show that neither of the usual closed formulas for Khintchine inequalities can work in L 2,∞. We also give an application to martingale inequalities