| Weighted Variation Inequalities for Commutators of One-Sided Singular Integrals |
| Received:August 20, 2022 Revised:January 08, 2023 |
| Key Words:
$\rho$-variation one-sided singular integral commutator one-sided weight one-sided Triebel-Lizorkin spaces
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| Fund Project:Supported by the National Natural Science Foundation of China (Grant No.12361019), the Natural Science Foundation of Xinjiang Uygur Autonomous Region (Grant No.2021D01C463) and YiLi Normal University's ``High-level Talents" Program of Academic Integrity (Grant No.YSXSJS22001). |
| Author Name | Affiliation | | Xin CHENG | School of Mathematics and Statistics, Yili Normal University, Xinjiang 835000, P. R. China | | Suixin HE | School of Mathematics and Statistics, Yili Normal University, Xinjiang 835000, P. R. China | | Jing ZHANG | 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. |
| Citation: |
| DOI:10.3770/j.issn:2095-2651.2023.05.004 |
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