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Weighted boundedness of fractional integrals associated with admissible functions on spaces of homogeneous type

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Abstract

Let \(({{\mathcal {X}}},d,\mu )\) be a space of homogeneous type in the sense of Coifman and Weiss. In this paper, we first establish several weighted norm estimates for various maximal functions. Then we show the weighted boundedness of the fractional integral \(I_\beta \) associated with admissible functions and its commutators. Similarly to \(I_\beta \), corresponding results for Calderón–Zygmund operators T associated with admissible functions are also included in this article.

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Acknowledgements

This project is supported by the National Natural Science Foundation of China (Grant Nos. 11701160 and 11871100). The authors would like to thank all the anonymous referees for their several enlightening comments on this article, which do improve the presentation of this article.

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Correspondence to Xing Fu.

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Qin, G., Fu, X. Weighted boundedness of fractional integrals associated with admissible functions on spaces of homogeneous type. Fract Calc Appl Anal (2024). https://doi.org/10.1007/s13540-024-00300-5

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