| B-Valued Dyadic Derivative |
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| 作者姓名： | ZHANG Chuanzhou CHEN Lihong LIU Peide |
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| 作者单位： | School of Mathematics and Statistics, Wuhan University,Wuhan 430072, Hubei, China |
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| 基金项目： | Supported by the National Natural Science Foundation of China（ 10671147） |
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| 摘 要： | The principles of the new maximal operator H＊ we defined are discussed. We prove that it is bounded from martingale Hardy-Lorentz L^Xp.q0,1） to the Lorentz L^Xp.q0,1） for 1/2〈 p〈∞, 0〈~ q ≤ ∞, where X is any Banach space. When the Banach space X has the RN property, the sequence dnHnf converges to f a.e. Meanwhile the convergence in L^Xp norm for 1≤p〈∞ is a consequence of that the family functions K （n∈N） is an approximate identity.
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| 关 键 词： | 鞅 并向量 二价积分 数学分析 |
| 文章编号： | 1007-1202（2007）06-0961-04 |
| 收稿时间： | 18 March 2007 |
| 修稿时间： | 2007-03-18 |
<Emphasis Type="Italic">B</Emphasis>-valued dyadic derivative |
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| ZHANG Chuanzhou CHEN Lihong,LIU Peide.B-Valued Dyadic Derivative[J].Wuhan University Journal of Natural Sciences,2007,12(6):961-964. |
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| Authors: | Zhang Chuanzhou Chen Lihong Liu Peide |
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| Institution: | (1) School of Mathematics and Statistics, Wuhan University, Wuhan, 430072, Hubei, China |
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| Abstract: | The principles of the new maximal operator H* we defined are discussed. We prove that it is bounded from martingale Hardy-Lorentz H
p,q
X
0,1) to the Lorentz L
p,q
X
0,1) for 1/2 < p<∞, 0<q⩽∞, where X is any Banach space. When the Banach space X has the RN property, the sequence d
n
H
n
f converges to f a.e. Meanwhile the convergence in L
p
X
norm for 1⩽p<∞ is a consequence of that the family functions K
n(n∈N) is an approximate identity.
Biography: ZHANG Chuanzhou(1978–), male, Ph.D. candidate, research direction: Banach space geometry and martingale theory. |
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| Keywords: | martingale Hardy space dyadic derivative dyadic integral |
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