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Algebras of Calderón–Zygmund Operators on Spaces of Homogeneous Type

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Abstract

In this paper, using continuous Calderón’s reproducing formulas, we obtain algebras of Calderón–Zygmund operators on spaces of homogenous type in the setting of both one parameter and bi-parameter. More precisely, all classical Calderón–Zygmund operators form an algebra when \(T(1)=T^*(1)=0\) and all product singular integral operators in Journé’s class form an algebra when \(T_1(1)=T_1^*(1)=T_2(1)=T_2^*(1)\,{=}\,0\).

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Acknowledgements

The first author is supported by the National Natural Science Foundation of China (No.11901495) and the Scientific Research Fund of Hunan Provincial Education Department (No.19A503). The third author is supported by the National Natural Science Foundation of China (No.12101222) and Hunan Provincial NSF Project (2021JJ40187).

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Authors and Affiliations

  1. School of Mathematics & Computational Science, Xiangtan University, Xiangtan, 411105, People’s Republic of China

    Fanghui Liao & Yan Wang

  2. School of Mathematics & Computational Science, Hunan University of Science and Technology, Xiangtan, 411201, People’s Republic of China

    Zhengyang Li

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  1. Fanghui Liao
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  2. Yan Wang
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  3. Zhengyang Li
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Correspondence to Zhengyang Li.

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Liao, F., Wang, Y. & Li, Z. Algebras of Calderón–Zygmund Operators on Spaces of Homogeneous Type. J Geom Anal 32, 126 (2022). https://doi.org/10.1007/s12220-021-00864-1

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