Acta mathematica scientia,Series B ›› 2009, Vol. 29 ›› Issue (2): 402-408.doi: 10.1016/S0252-9602(09)60039-4

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TWO-WEIGHT WEAK-TYPE MAXIMAL INEQUALITIES FOR MARTINGALES

Ren Yanbo, Hou Youliang   

  1. Department of Mathematics &|Physics, Henan University of Science and Technology, Luoyang 471003, China
  • Received:2006-11-28 Online:2009-03-20 Published:2009-03-20
  • Supported by:

    Sponsored by the National NSFC (10671147)

Abstract:

In this article, some necessary and sufficient conditions are shown in order that the inequality of the form
Φ1(λ)Pu(f* > λ) ≤ Ev2(C|f|))
holds with some constant C > 0 independent of martingale f = (fn)n≥0 and λ > 0, where Φ1 and Φ2 are a pair of Young functions, f* = sup|fn| and f = limfn a.e.

Key words: Martingale, weight, weak-type inequality, Young function

CLC Number: 

  • 60G42
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