| Bochner—Riesz算子及其高阶交换子L^p有界的必要条件 |
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| 引用本文： | 夏霞. Bochner—Riesz算子及其高阶交换子L^p有界的必要条件[J]. 应用泛函分析学报, 2009, 11(4): 377-382 |
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| 作者姓名： | 夏霞 |
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| 作者单位： | 天津师范大学数学科学学院,天津,300387 |
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| 基金项目： | 国家自然科学基金，北京市自然科学基金，天津师范大学引进人才基金 |
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| 摘 要： | 通过选择适当的L^p函数并应用连续分解方法，给出了低于临界阶的Bochner—Riesz算子在L^p空间有界的新的证明，同时得到了该算子和Lipschitz函数构成的高阶交换子L^p有界性的必要条件．
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| 关 键 词： | 低于临界阶的Bochner—Riesz算子 交换子 Lipschitz函数 L^p空间 |
Necessary Condition Boundedness of Bochner-Riesz Operator and Its Higher Commutators |
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| XIA Xia. Necessary Condition Boundedness of Bochner-Riesz Operator and Its Higher Commutators[J]. Acta Analysis Functionalis Applicata, 2009, 11(4): 377-382 |
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| Authors: | XIA Xia |
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| Affiliation: | XIA Xia (School of Mathematical Sciences, Tianjin Normal University, Tianjin 300387, China ) |
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| Abstract: | In terms of continuous decomposition and choosing an appropriate L~p function, the author poses a new method to prove the necessary condition for L~p boundedness of Bochner-Riesz operators below the critical index. And a similar necessary condition for L~p-boundedness of higher order commutators generated by Bochner-Riesz operators below the critical index and Lipschitz functions is obtained by this method. |
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| Keywords: | Bochner-Riesz operator below critical index commutator Lipsehitz function L~p space |
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