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On the BMO boundedness of the Cauchy integral on a chord-arc curve

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Abstract

A detailed proof is given for the boundedness of the Cauchy integral acting on BMO on a chord-arc curve. Some applications are given to the Faber operator on BMOA and to the jump problem for BMO.

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Acknowledgements

The first author would like to thank Professor G. David for useful conversation.

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  1. Department of Mathematics, Soochow University, Suzhou, 215006, People’s Republic of China

    Liu Tailiang & Shen Yuliang

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  1. Liu Tailiang
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  2. Shen Yuliang
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Correspondence to Shen Yuliang.

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Research supported by the National Natural Science Foundation of China (Grant No. 12171346).

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Tailiang, L., Yuliang, S. On the BMO boundedness of the Cauchy integral on a chord-arc curve. Arch. Math. 120, 203–212 (2023). https://doi.org/10.1007/s00013-022-01806-1

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