| Boundedness of Commutators with Lipschitz Functions in Non-homogeneous Spaces |
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| 作者姓名： | Xiaoli FU Yan MENG Dachun YANG |
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| 作者单位： | Xiaoli FU Yan MENG Dachun YANG School of Mathematical Sciences，Beijing Normal University，Beijing 100875，China. School of Mathematical Sciences，Beijing Normal University，Beijing 100875，China; School of Information，Renmin University，Beijing 100872，China. Corresponding author. School of Mathematical Sciences，Beijing Normal University，Beijing 100875，China. |
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| 摘 要： | Under the assumption that the underlying measure is a non-negative Radon measure which only satisfies some growth condition, the authors prove that for a class of commutators with Lipschitz functions which include commutators generated by Calderon-Zygmund operators and Lipschitz functions as examples, their boundedness in Lebesgue spaces or the Hardy space H1 (μ) is equivalent to some endpoint estimates satisfied by them. This result is new even when the underlying measureμis the d-dimensional Lebesgue measure.
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| 关 键 词： | 换向器 Lipschitz函数 非均匀空间 Lebesgue空间 Hardy空间 |
| 收稿时间： | 7/5/2015 12:00:00 AM |
Boundedness of Commutators with Lipschitz Functions in Non-homogeneous Spaces |
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| Xiaoli FU,Yan MENG,Dachun YANG.Boundedness of Commutators with Lipschitz Functions in Non-homogeneous Spaces[J].Chinese Annals of Mathematics,Series B,2007,28(1):67-80. |
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| Authors: | Xiaoli FU Yan MENG and Dachun YANG |
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| Institution: | 1. School of Mathematical Sciences, Beijing Normal University, Beijing 100875, China
2. School of Mathematical Sciences, Beijing Normal University, Beijing 100875, China;School of Information, Renmin University, Beijing 100872, China |
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| Abstract: | Abstract
Under the assumption that the underlying measure is a non-negative Radon measure which only satisfies some growth condition,
the authors prove that for a class of commutators with Lipschitz functions which include commutators generated by Calderón-Zygmund
operators and Lipschitz functions as examples, their boundedness in Lebesgue spaces or the Hardy space H
1(μ) is equivalent to some endpoint estimates satisfied by them. This result is new even when the underlying measure μ is the d-dimensional Lebesgue measure.
* Project supported by the National Natural Science Foundation of China (No. 10271015) and the Program for New Century Excellent
Talents in Universities of China (No. NCET-04-0142). |
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| Keywords: | Commutator Lipschitz function Lebesgue space Hardy space RBMO space Non-doubling measure |
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