数学物理学报(英文版)

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WEIGHTED AVERAGE OF DIRICHLET KERNELS FOR VILENKIN-LIKE SYSTEM

张传洲; 刘培德   

  1. School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China College of Science, Wuhan University of Science and Technology, Wuhan 430065, China
  • 收稿日期:1900-01-01 修回日期:1900-01-01 出版日期:2009-02-20 发布日期:2009-02-20
  • 通讯作者: 张传洲
  • 基金资助:
    Sponsored by the National NSFC under grant No.10671147 and by Foundation of Hubei Scientific Committee under grant No.B20081102

WEIGHTED AVERAGE OF DIRICHLET KERNELS FOR VILENKIN-LIKE SYSTEM

Zhang Chuanzhou; Liu Peide   

  1. School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China College of Science, Wuhan University of Science and Technology, Wuhan 430065, China
  • Received:1900-01-01 Revised:1900-01-01 Online:2009-02-20 Published:2009-02-20
  • Contact: Zhang Chuanzhou

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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 (H*p(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.

关键词: Martingale Hardy space, Vilenkin-like systems, weighted average

Abstract: 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 (H*p(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.

Key words: Martingale Hardy space, Vilenkin-like systems, weighted average

中图分类号: 

  • 60G46
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