| WEIGHTED INEQUALITIES FOR THE GEOMETRIC MAXIMAL OPERATOR ON MARTINGALE SPACES |
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| 作者姓名： | 左红亮 刘培德 |
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| 作者单位： | [1]College of Mathematics and Information Science, Henan Normal University, Xinxiang 453007, China [2]College of Mathematics and Statistics, Wuhan University, Wuhan 430072, China |
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| 基金项目： | This work was supported by the NSF of China and the aid financial plan for the backbone of the young teachers of university of Henan |
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| 摘 要： | In this article, the authors introduce two operators-geometrical maximal operator Mo and the closely related limiting operator M0^＊, then they give sufficient conditions under which the equality M0=MM0^＊ holds, and characterize the equivalent relations between the weak or strong type weighted inequality and the property of W∞-weight or W∞^＊-weight for the geometrical maximal operator in the case of two-weight condition. What should be mentioned is that the new operator-the geometrical minimal operator is equal to the limitation of the minimal operator sequence, and the results for the minimal operator proved in 12] makes the proof elegant and evident.
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| 关 键 词： | 几何算子 不等式 弓式接线 操控室 |
| 收稿时间： | 2005-08-28 |
Weighted Inequalities for the Geometric Maximal Operator on Martingale Spaces |
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| Zuo Hongliang,Liu Peide,.WEIGHTED INEQUALITIES FOR THE GEOMETRIC MAXIMAL OPERATOR ON MARTINGALE SPACES[J].Acta Mathematica Scientia,2008,28(1):81-85. |
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| Authors: | Zuo Hongliang Liu Peide |
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| Institution: | aCollege of Mathematics and Information Science, Henan Normal University, Xinxiang 453007, China;bCollege of Mathematics and Statistics, Wuhan University, Wuhan 430072, China |
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| Abstract: | In this article, the authors introduce two operators-geometrical maximal operator Mo and the closely related limiting operator M*O, then they give sufficient conditions under which the equality MO = M*O holds, and characterize the equivalent relations between the weak or strong type weighted inequality and the property of W∞-weight or W*∞-weight for the geometrical maximal operator in the case of two-weight condition. What should be mentioned is that the new operator-the geometrical minimal operator is equal to the limitation of the minimal operator sequence, and the results for the minimal operator proved in 12] makes the proof elegant and evident. |
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| Keywords: | Geometric maximal operator weight martingale inequality |
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