Abstract
In this paper, the authors first discuss the characterization of Herz Triebel–Lizorkin spaces with variable exponent via two families of operators. By this characterization, the authors prove that the Lipschitz commutators of sublinear operators is bounded from Herz spaces with variable exponent to Herz Triebel–Lizorkin spaces with variable exponent. As applications, the corresponding boundedness estimates for the commutators of maximal operator, Riesz potential operator and Calderón–Zygmund operator are established.
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Acknowledgements
The authors would like to thank the referee for her/his careful reading of the manuscript and giving so many constructive comments which indeed improve the presentation of this article.
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This project is supported by the National and Regional Natural Science Foundation of China (12261083) and the National Natural Science Foundation of Xinjiang Province of China (No. 2021D01C463).
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Fang, C., Wei, Y. & Zhang, J. The Boundedness of Commutators of Sublinear Operators on Herz Triebel–Lizorkin Spaces with Variable Exponent. Results Math 78, 71 (2023). https://doi.org/10.1007/s00025-023-01843-4
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DOI: https://doi.org/10.1007/s00025-023-01843-4