Noncommutative martingale Hardy-Orlicz spaces: Dualities and inequalities.

We investigate dualities and inequalities related to noncommutative martingale Hardy-Orlicz spaces. More precisely, for a concave Orlicz function Φ, we characterize the dual spaces of noncommutative martingale Hardy-Orlicz spaces H Φ c (ℛ) and h Φ c (ℳ) , where ℛ denotes a hyperfinite finite von Neumann algebra and ℳ is a finite von Neumann algebra. The first duality is new even for classical martingales, which partially answers the problem raised by Conde-Alonso and Parcet (2016). We establish as well asymmetric martingale inequalities associated with Orlicz functions that are p-convex and q-concave for 0 < p ≼ q < 2. [ABSTRACT FROM AUTHOR]