Resumen de On certain martingale inequalities for maximal functions and mean oscillations

Masato Kikuchi, Yasuhiro Kinoshita

• Let X be a Banach function space over a nonatomic probability space. For a uniformly integrable martingale f=(fn) with respect to a filtration F=(Fn), let Mf=supn|fn| and θFf=supnE[|f∞−fn−1|∣Fn]. We give a necessary and sufficient condition on X for the inequality ∥θFf∥X≤C∥Mf∥X to hold.