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WEIGHTED AVERAGE OF DIRICHLET KERNELS FOR VILENKIN-LIKE SYSTEM 被引量:1

WEIGHTED AVERAGE OF DIRICHLET KERNELS FOR VILENKIN-LIKE SYSTEM
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摘要 For Vilenkin-like system, the authors define a new operator H*f := supn |Hnf|, where Hnf is the weighted average for partial sums, and prove that H* is of type (Hp* (Gm), Lp(Gm)) for all 1/2 < p ≤ ∞. As a consequence, the authors prove the operator S*f := supn |Snf| is of type (p, p) for 1 < p < ∞, where Snf is the n-partial sum. For Vilenkin-like system, the authors define a new operator H*f := supn |Hnf|, where Hnf is the weighted average for partial sums, and prove that H* is of type (Hp* (Gm), Lp(Gm)) for all 1/2 < p ≤ ∞. As a consequence, the authors prove the operator S*f := supn |Snf| is of type (p, p) for 1 < p < ∞, where Snf is the n-partial sum.
出处 《Acta Mathematica Scientia》 SCIE CSCD 2009年第1期45-55,共11页 数学物理学报(B辑英文版)
基金 Sponsored by the National NSFC under grant No10671147 Foundation of Hubei Scientific Committee under grant NoB20081102
关键词 Martingale Hardy space Vilenkin-like systems weighted average Martingale Hardy space Vilenkin-like systems weighted average
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