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《Acta Analysis Functionalis Applicata》 2009-01
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Atomic Decompositions on Some B-valued Quasi-martingale Spaces

WANG Jun-jun1,2, HOU You-liang1 1. School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China 2. School of Mathematics and Statistics, Pingdingshan University, Pingdingshan 467002, China  
Let 1p≤2, 0α≤1 and X a p-uniformly smoothable Banach space, then for each X-valued quasi-martingale f=fnn≥0∈pHσαX, f can be decomposed into fn=sum form k∈Z to μkank(n≥0) and ‖f‖pHασ(X)+‖Rf‖α~inf(sum form k∈Z to μkα)1/α, where ak=(ank)n≥0(k∈Z) is a sequence of 1, α, ∞; p quasi-martingale atoms with supk∈Z‖ak*‖α∞ and μkk∈Z∈lα are nonnegative numbers. The similar results hold for quasi-martingale spaces pHαS(X) and pKα(X). Moreover, by using the theorems of atomic decompositions of quasi-martingales we prove some quasi-martingale inequalities.
【Fund】: 国家自然科学基金资助项目(10371093)
【CateGory Index】: O211.6
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