Abstract
Let \((\mathcal {X},\rho ,\mu )\) be Ahlfors-1 regular metric spaces. By developing the Littlewood–Paley characterization of Lipschitz spaces over \((\mathcal {X},\rho ,\mu )\) and establishing a density argument in the weak sense, the authors give a necessary and sufficient condition for the boundedness of Calderón–Zygmund operators on the Lipschitz spaces.
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Acknowledgements
This research was supported by National Natural Science Foundation of China (Grant No.11626213, 11771399), Zhejiang Provincial Natural Science Foundation of China (Grant No. LQ17A010002), Zhejiang Provincial Xinmiao Talents Program (Grant No. 2018R415037) and China Scholarship Council(Grant No. 201808330176).
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Zheng, T., Li, H. & Tao, X. The Boundedness of Calderón–Zygmund Operators on Lipschitz Spaces Over Spaces of Homogeneous Type. Bull Braz Math Soc, New Series 51, 653–669 (2020). https://doi.org/10.1007/s00574-019-00169-6
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DOI: https://doi.org/10.1007/s00574-019-00169-6