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Two-weighted estimates for multilinear Hausdorff operators and commutators on stratified groups

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Abstract

In this paper, we study the multilinear Hausdorff operators and their commutators on stratified groups. We obtain some sufficient and necessary conditions for the boundedness of multilinear Hausdorff operators on two-weighted central Morrey spaces, two-weighted Herz spaces and two-weighted Morrey-Herz spaces. Furthermore, some sufficient conditions for the boundedness of commutators generated by multilinear Hausdorff operators and weighted central BMO functions on such spaces are shown.

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Acknowledgements

The authors would like to thank the referees for their careful reading and useful suggestions, which have improved the paper.

Funding

This work was supported by Beijing Municipal Natural Science Foundation (Grant No.1222008) and the National Natural Science Foundation of China (Grant No.12271042) and the National Key Research and Development Program of China (Grant No.2020YFA0712900).

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Author notes

  1. Yingjie Sun and Jiman Zhao contributed equally to this study.

Authors and Affiliations

  1. Department of Mathematics and Physics Teaching, Taishan College of Science and Technology, Taian, 271002, China

    Yingjie Sun

  2. School of Mathematical Sciences, Beijing Normal University, Beijing, 100875, China

    Yingjie Sun & Jiman Zhao

Authors
  1. Yingjie Sun
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  2. Jiman Zhao
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Correspondence to Jiman Zhao.

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Sun, Y., Zhao, J. Two-weighted estimates for multilinear Hausdorff operators and commutators on stratified groups. J. Pseudo-Differ. Oper. Appl. 13, 49 (2022). https://doi.org/10.1007/s11868-022-00480-9

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  • DOI: https://doi.org/10.1007/s11868-022-00480-9

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