Analysis of Banach function spaces in view point of martingale theory

  • 菊池, 万里 (Principal Investigator)
  • 久保, 文夫 (Co-Investigator(Kenkyū-buntansha))
  • 和泉澤, 正隆 (Co-Investigator(Kenkyū-buntansha))

Project Details

Abstract

・ Let f =(f_n) be a martingale and let Φ:R→[0,∞) be a convex function such that Φ(0) =0 and Φ(t)=Φ(-t) for all t≧0. Because Φ(f) =(Φ(f_n)) is a submartingale, it can be decomposed into a sum of a martingale g=(gn) and a predictable increasing process h=(h_n) such that h_0=0 (Doob decomposition). We established a characterization of those Banach function spaces X for which the inequalities‖h_∞‖x≦C_x,_Φ‖Mf‖x and sup_n‖g_n‖x≦C_x,_Φ‖Mf‖x hold.
StatusFinished
Effective start/end date2005/01/01 → 2007/12/31

Funding

  • Japan Society for the Promotion of Science: ¥2,970,000.00

Keywords

  • マルチンゲール
  • Banach関数空間
  • 再配分不変空間
  • ノルム不等式
  • Boyd index
  • Banach 関数空間
  • martingale
  • Banach function space
  • rearrangement-invariant space
  • norm inequality

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