On certain martingale inequalities for maximal functions and mean oscillations

Authors

  • Masato Kikuchi
  • Yasuhiro Kinoshita

DOI:

https://doi.org/10.7146/math.scand.a-15191

Abstract

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=sup and \theta_{\mathcal F}f=\sup_n E[|f_{\infty}- f_{n-1}| \mid{\mathcal F}_n]. We give a necessary and sufficient condition on X for the inequality \parallel \theta_{\mathcal F}f \parallel_X \leq C\parallel Mf\parallel_X to hold.

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Published

2011-12-01

How to Cite

Kikuchi, M., & Kinoshita, Y. (2011). On certain martingale inequalities for maximal functions and mean oscillations. MATHEMATICA SCANDINAVICA, 109(2), 309–319. https://doi.org/10.7146/math.scand.a-15191

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Articles