WEIGHTED AVERAGE OF DIRICHLET KERNELS FOR VILENKIN-LIKE SYSTEM

doi:10.1016/S0252-9602(09)60005-9

数学物理学报(英文版)

WEIGHTED AVERAGE OF DIRICHLET KERNELS FOR VILENKIN-LIKE SYSTEM

张传洲; 刘培德

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

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

摘要/Abstract

摘要： For Vilenkin-like system, the authors define a new operator H* f:=sup_n|H_nf|, where H_nf is the weighted average for partial sums, and prove that H* is of type (H*p(G_m), L_p(G_m)) for all 1/2 < p ≤ ∞ . As a consequence, the authors prove the operator S*f:=sup_n|S_nf| is of type (p, p) for 1<p< ∞, where S_nf 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:=sup_n|H_nf|, where H_nf is the weighted average for partial sums, and prove that H* is of type (H*_p(G_m), L_p(G_m)) for all 1/2 < p ≤ ∞ . As a consequence, the authors prove the operator S*f:=sup_n|S_nf| is of type (p, p) for 1<p< ∞, where S_nf is the n-partial sum.

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

中图分类号:

60G46

张传洲; 刘培德. WEIGHTED AVERAGE OF DIRICHLET KERNELS FOR VILENKIN-LIKE SYSTEM[J]. 数学物理学报(英文版), 2009, 29(1): 45-55.

Zhang Chuanzhou; Liu Peide. WEIGHTED AVERAGE OF DIRICHLET KERNELS FOR VILENKIN-LIKE SYSTEM[J]. Acta mathematica scientia,Series B, 2009, 29(1): 45-55.

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WEIGHTED AVERAGE OF DIRICHLET KERNELS FOR VILENKIN-LIKE SYSTEM

WEIGHTED AVERAGE OF DIRICHLET KERNELS FOR VILENKIN-LIKE SYSTEM

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