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The jump problem for the critical Besov space

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Abstract

We introduce the critical Besov space \( B_{p} \) on quasicircles and prove the solvability of the jump problem on d-regular quasicircles with \( B_{p} \) boundary values for \( d<p<\frac{d}{d-1}\). As applications, we obtain the \( B_{p}\, (1<p<\infty ) \) boundedness of the Cauchy integral operator and the Faber operator on chord-arc curves.

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Acknowledgements

The authors would like to thank Professor Han Yongsheng for his suggestions and comments. They would also like to thank the referee for a very careful reading of the manuscript and for several corrections which improves the presentation of the paper.

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  1. Tailiang Liu

    Present address: School of Mathematics and Physics, Jiangsu University of Technology, Changzhou, People’s Republic of China

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

    Tailiang Liu & Yuliang Shen

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  1. Tailiang Liu
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Correspondence to Yuliang Shen.

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Liu, T., Shen, Y. The jump problem for the critical Besov space. Math. Z. 306, 59 (2024). https://doi.org/10.1007/s00209-024-03462-3

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