| 极大变指标Herz空间上的参数型粗糙核Littlewood-Paley算子 |
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| 引用本文： | 史鹏伟,陶双平. 极大变指标Herz空间上的参数型粗糙核Littlewood-Paley算子[J]. 山东大学学报(理学版), 2022, 57(12): 45-54. DOI: 10.6040/j.issn.1671-9352.0.2021.685 |
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| 作者姓名： | 史鹏伟 陶双平 |
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| 作者单位： | 西北师范大学数学与统计学院, 甘肃 兰州 730070 |
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| 基金项目： | 国家自然科学基金项目(12161080) |
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| 摘 要： | 借助变指标Lebesgue空间上的有界性,利用函数分层分解和实变技巧,得到了参数型粗糙核Marcinkiewicz积分、面积积分和 Littlewood-Paley g*λ函数在极大变指标Herz空间上的有界性。同时也证明了面积积分和Littlewood-Paley g*λ函数高阶交换子的有界性。
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| 关 键 词： | 极大变指标Herz空间 粗糙核 参数型Littlewood-Paley算子 高阶交换子 |
Parameterized Littlewood-Paley operators with rough kernel on grand variable Herz spaces |
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| SHI Peng-wei,TAO Shuang-ping. Parameterized Littlewood-Paley operators with rough kernel on grand variable Herz spaces[J]. Journal of Shandong University, 2022, 57(12): 45-54. DOI: 10.6040/j.issn.1671-9352.0.2021.685 |
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| Authors: | SHI Peng-wei TAO Shuang-ping |
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| Affiliation: | College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, Gansu, China |
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| Abstract: | With the help of the boundedness of the Lebesgue space with variable exponent, by applying hierarchical decomposition of function and real variable techniques, the boundedness of the parameterized Marcinkiewicz integral, the area integral and Littlewood-Paley g*λ function with rough kernel is obtained on grand variable Herz spaces. Meanwhile, the boundedness of higher order commutators generated by the area integral and Littlewood-Paley g*λ function is also proved on grand variable Herz spaces. |
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| Keywords: | grand variable Herz space rough kernel parameterized Littlewood-Paley operator higher order commutator |
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