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| 摘要: |
| 本文研究二维Hardy空间维林肯型系统的极大算子的有界性.利用原子分解方法, 我们证明二维极大算子Tαf:=sup2-α≤n/m≤2α|f*Pn,m|是从鞅Hardy空间Hp到Lp有界的，其中0<p<1/2,α≥0. 作为应用,我们得到二维极大算子σ*f=sup2-α≤n/m≤2α|σ˜n,mf|/[(n+1)(m+1)]1/p-2的有界性证明.通过构造反例，我们证明二维极大算子σˆ*f=supn,m∈N|σn,mf|/[(n+1)(m+1)]1/p-2不是从鞅Hardy空间Hp到Lp有界的, 其中0<p<1/2. 上述结果推广了沃尔什系统、维林肯系统下的已知结论. |
| 关键词: 维林肯型系统 极大算子 Dirichlet核 Fejé r核 |
| DOI： |
| 分类号:O174.2 |
| 基金项目: |
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| TWO-DIMENSIONAL MAXIMAL OPERATOR OF VILENKIN-LIKE SYSTEM ON HARDY SPACES |
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ZHANG Xue-ying,WANG Chao-yue,ZHANG Chuan-zhou,XIAO Jun
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| Abstract: |
| In this paper, we research the boundedness of two-dimensional maximal operator of Vilenkin-like system on Hardy spaces. By means of atomic decomposition, the two-dimensional maximal operator Tαf:=sup2-α≤n/m≤2α|f*Pn,m| is bounded from Hp to Lp, where 0<p<1/2 and α≥0. As an application, we prove the boundedness of two-dimensional operator σ*f=sup2-α≤n/m≤2α|σ˜n,mf|/[(n+1)(m+1)]1/p-2. By a counterexample, we also prove that two dimensional maximal operator σˆ*f=supn,m∈N|σn,mf|/[(n+1)(m+1)]1/p-2 is not bounded from Hp to Lp, where 0<p<1/2. The results as above generalize the known conclusions in Walsh system or in Vilenkin system. |
| Key words: Vilenkin-like system maximal operator Dirichlet kernels Fejé r kernels |
