| 摘要: |
| 本文研究了二进求导极大算子的有界性.利用狄利克雷核的重要性质,构造了反例证明此极大算子在一维和二维情况下都不是从Hardy空间Hn到Hardy空间Hp有界的,其中0＜p≤1.此结果说明文献[4]中的结论是不正确的. |
| 关键词: Hardy空间 二进导数 二进积分 |
| DOI： |
| 分类号:O174.2 |
| 基金项目:Supported by Hubei Province Key Laboratory of Systems Science in Metal-lurgical Process(Wuhan University of Science and Technology)(C201016); National Natural Science Foundation of Pre-Research Item(2011XG005) |
|
| THE BOUNDEDNESS OF TWO-DIMENSIONAL MAXIMAL OPERATOR OF DYADIC DERIVATIVE |
|
ZHANG Xue-ying,YU Xiao-hong,ZHANG Chuan-zhou
|
|
ZHANG Xue-ying1,YU Xiao-hong2,ZHANG Chuan-zhou1(1.College of Science,Wuhan University of Science and Technology,Wuhan 430065,China)(2.Dept.of Math.,Luoyang Institute of Science and Technology,Luoyang 471023,China)
|
| Abstract: |
| In this paper, we consider the maximal operator of dyadic derivative. By using property of Dirichlet kernel, we construct a counter-example to prove that the one- and two-dimensional maximal operators are not bounded from the Hardy space Hp to the Hardy space Hp for 0 ＜ p ≤ 1. These results enrich some known conclusions and point out that the conclusion in[4] is incorrect. |
| Key words: Hardy spaces dyadic derivative dyadic integral |
