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=supn|fn| and θFf=supnE[|ffn1|Fn]. We give a necessary and sufficient condition on X for the inequality θFfXCMfX 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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Section

Articles