WEIGHTED AVERAGE OF DIRICHLET KERNELS FOR VILENKIN-LIKE SYSTEM

Zhang Chuanzhou; Liu Peide

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

Acta mathematica scientia, Series B >

2009 , Vol. 29 >Issue 1: 45 - 55

DOI: https://doi.org/10.1016/S0252-9602(09)60005-9

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WEIGHTED AVERAGE OF DIRICHLET KERNELS FOR VILENKIN-LIKE SYSTEM

Zhang Chuanzhou ,
Liu Peide

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School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China College of Science, Wuhan University of Science and Technology, Wuhan 430065, China

Received date: 1900-01-01

Revised date: 1900-01-01

Online published: 2009-02-20

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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

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Zhang Chuanzhou , Liu Peide . WEIGHTED AVERAGE OF DIRICHLET KERNELS FOR VILENKIN-LIKE SYSTEM[J]. Acta mathematica scientia, Series B, 2009 , 29(1) : 45 -55 . DOI: 10.1016/S0252-9602(09)60005-9

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