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Characterizations for boundedness of fractional maximal function commutators in variable Lebesgue spaces on stratified groups

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Abstract

In this paper, the main aim is to consider the mapping properties of the maximal or nonlinear commutator for the fractional maximal operator with the symbols belong to the Lipschitz spaces on variable Lebesgue spaces in the context of stratified Lie groups, with the help of which some new characterizations to the Lipschitz spaces and nonnegative Lipschitz functions are obtained in the stratified groups context. Meanwhile, some equivalent relations between the Lipschitz norm and the variable Lebesgue norm are also given.

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Acknowledgements

The authors cordially thank the anonymous referees who gave valuable suggestions and useful comments which have lead to the improvement of this paper.

Funding

This work was completed with the support of the Scientific Research Fund (Nos. S022022177, 2023AH050940) for Zhao and the Science and Technology Fund of HLJ (Nos. 1453ZD031, 2019-KYYWF-0909) for Wu.

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Author notes

  1. Wenjiao Zhao and Jianglong Wu have contributed equally to this work.

Authors and Affiliations

  1. School of Mathematics, Physics and Finance, Anhui Polytechnic University, Wuhu, 241000, China

    Wenjiao Zhao

  2. Department of Mathematics, Mudanjiang Normal University, Mudanjiang, 157011, China

    Jianglong Wu

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  1. Wenjiao Zhao
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  2. Jianglong Wu
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Correspondence to Jianglong Wu.

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Communicated by Kehe Zhu.

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Zhao, W., Wu, J. Characterizations for boundedness of fractional maximal function commutators in variable Lebesgue spaces on stratified groups. Ann. Funct. Anal. 15, 34 (2024). https://doi.org/10.1007/s43034-024-00334-z

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