On certain martingale inequalities for maximal functions and mean oscillations

• Autores: Masato Kikuchi, Yasuhiro Kinoshita
• Localización: Mathematica scandinavica, ISSN 0025-5521, Vol. 109, Nº 2, 2011, págs. 309-319
• Idioma: inglés
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• Resumen

  • 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.