Acta mathematica scientia, Series B >
TWO-WEIGHT WEAK-TYPE MAXIMAL INEQUALITIES FOR MARTINGALES
Received date: 2006-11-28
Online published: 2009-03-20
Supported by
Sponsored by the National NSFC (10671147)
In this article, some necessary and sufficient conditions are shown in order that the inequality of the form
Φ1(λ)Pu(f* > λ) ≤ Ev(Φ2(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
Ren Yanbo , Hou Youliang . TWO-WEIGHT WEAK-TYPE MAXIMAL INEQUALITIES FOR MARTINGALES[J]. Acta mathematica scientia, Series B, 2009 , 29(2) : 402 -408 . DOI: 10.1016/S0252-9602(09)60039-4
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