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Ahlfors-regular curves and Carleson measures

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Abstract

We study the relation between the boundary of a simply connected domain Ω being Ahlfors-regular and the invariance of Carleson measures under the push-forward operator induced by a conformal mapping from the unit disk Δ onto the domain Ω. As an application, we characterize the chord-arc curves with small norms and the asymptotically smooth curves in terms of the complex dilatation of some quasiconformal reflection with respect to the curve.

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Acknowledgements

This work was supported by National Natural Science Foundation of China (Grant No. 11501259). The authors thank the referees for a very careful reading of the manuscript and for sentence-by-sentence corrections. The first author thanks Professor Yuliang Shen for pointing out an error in the first draft of this paper.

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Correspondence to Huaying Wei.

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Wei, H., Zinsmeister, M. Ahlfors-regular curves and Carleson measures. Sci. China Math. 63, 1057–1064 (2020). https://doi.org/10.1007/s11425-018-9420-2

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  • DOI: https://doi.org/10.1007/s11425-018-9420-2

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