| 单边奇异积分交换子的加权变差不等式 |
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| 引用本文： | 程鑫,何随心,张婧.单边奇异积分交换子的加权变差不等式[J].数学研究及应用,2023,43(5):542-556. |
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| 作者姓名： | 程鑫 何随心 张婧 |
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| 作者单位： | 伊犁师范大学数学与统计学院, 新疆 伊犁 835000;伊犁师范大学数学与统计学院, 新疆 伊犁 835000; 伊犁师范大学应用数学研究所, 新疆 伊犁 835000 |
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| 基金项目： | 国家自然科学基金(Grant No.12361019),新疆维吾尔自治区自然科学基金(Grant No.2021D01C463),伊犁师范大学``学实高层次人才岗位''项目(Grant No.YSXSJS22001). |
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| 摘 要： | 本文主要研究了单边Calder\''{o}n-Zygmund奇异积分交换子的加权变差不等式,即建立了单边Calder\''{o}n-Zygmund奇异积分与Lipschitz函数生成的交换子的加权变差不等式, 同时,利用权的外推法得到了该交换子在Triebel-Lizorkin空间上的加权变差不等式.
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| 关 键 词： | $\rho-$变差 单边奇异积分 单边权 交换子 单边Triebel-Lizorkin空间 |
| 收稿时间： | 2022/8/20 0:00:00 |
| 修稿时间： | 2023/1/8 0:00:00 |
Weighted Variation Inequalities for Commutators of One-Sided Singular Integrals |
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| Xin CHENG,Suixin HE,Jing ZHANG.Weighted Variation Inequalities for Commutators of One-Sided Singular Integrals[J].Journal of Mathematical Research with Applications,2023,43(5):542-556. |
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| Authors: | Xin CHENG Suixin HE Jing ZHANG |
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| Institution: | School of Mathematics and Statistics, Yili Normal University, Xinjiang 835000, P. R. China; School of Mathematics and Statistics, Yili Normal University, Xinjiang 835000, P. R. China; Institute of Applied Mathematics, Yili Normal University, Xinjiang 835000, P. R. China |
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| Abstract: | The paper is devoted to investigating the weighted variation inequalities for one-sided Calder\''on-Zygmund singular integral commutators. To be precise, we establish weighted variation inequalities for commutators generated by one-sided Calder\''on-Zygmund singular integral operators and Lipschitz functions. Moreover, using extrapolation of one-sided weights, the boundedness of the variation operators for these commutators is established on one-sided Triebel-Lizorkin spaces. |
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| Keywords: | $\rho$-variation one-sided singular integral commutator one-sided weight one-sided Triebel-Lizorkin spaces |
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