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Calderón–Zygmund Operators on Homogeneous Product Lipschitz Spaces

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The purpose of this paper is to establish a necessary and sufficient condition for the boundedness of product Calderón–Zygmund singular integral operators introduced by Journé on the product Lipschitz spaces. The key idea used in this paper is to develop the Littlewood–Paley theory for the product spaces which includes the characterization of a special product Besov space and a density argument for the product Lipschitz spaces in the weak sense.

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Authors and Affiliations

  1. Department of Mathematics, Zhejiang University of Science and Technology, Hangzhou, 310023, China

    Taotao Zheng & Xiangxing Tao

  2. Department of Mathematics, Zhejiang Normal University, Jinhua, 321004, China

    Jiecheng Chen, Jiawei Dai & Shaoyong He

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  1. Taotao Zheng
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  2. Jiecheng Chen
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  3. Jiawei Dai
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  4. Shaoyong He
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  5. Xiangxing Tao
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Correspondence to Shaoyong He.

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This research was supported by Zhejiang Provincial Natural Science Foundation of China (Grant No. LQ17A010002), National Natural Science Foundation of China (Grant Nos. 11626213, 11771399), Zhejiang Provincial Xinmiao Talents Program (Grant No. 2018R415037) and China Scholarship Council (Grant No. 201808330176).

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Zheng, T., Chen, J., Dai, J. et al. Calderón–Zygmund Operators on Homogeneous Product Lipschitz Spaces. J Geom Anal 31, 2033–2057 (2021). https://doi.org/10.1007/s12220-019-00331-y

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  • DOI: https://doi.org/10.1007/s12220-019-00331-y

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