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Limiting weak-type behaviors for Riesz transforms and maximal operators in Bessel setting

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Abstract

We establish the limiting weak type behaviors of Riesz transforms associated to the Bessel operators on ℝ+; which are closely related to the best constants of the weak type (1; 1) estimates for such operators. Meanwhile, the corresponding results for Hardy-Littlewood maximal operator and fractional maximal operator in Bessel setting are also obtained.

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Acknowledgements

This work was supported in part by the National Natural Science Foundation of China (Grant Nos. 11771358, 11871101).

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Authors and Affiliations

  1. School of Mathematics and Statistics, Linyi University, Linyi, 276005, China

    Xianming Hou

  2. School of Mathematical Sciences, Xiamen University, Xiamen, 361005, China

    Huoxiong Wu

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  1. Xianming Hou
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  2. Huoxiong Wu
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Correspondence to Huoxiong Wu.

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Hou, X., Wu, H. Limiting weak-type behaviors for Riesz transforms and maximal operators in Bessel setting. Front. Math. China 14, 535–550 (2019). https://doi.org/10.1007/s11464-019-0774-8

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  • DOI: https://doi.org/10.1007/s11464-019-0774-8

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