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A Restriction Estimate for a Certain Surface of Finite Type in \({\mathbb {R}}^3\)

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Abstract

In this paper, we study the restriction estimate for a certain surface of finite type in \({\mathbb {R}}^3\), and partially improve the results of Buschenhenke–Müller–Vargas (Anal PDE 10:817–891, 2017). The key ingredients of the proof include the so-called generalized rescaling technique based on a decomposition adapted to finite type geometry, a decoupling inequality and reduction of dimension arguments.

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Acknowledgements

We thank the anonymous referees and the associate editor for their invaluable comments which helped to improve the paper. C. Miao and J. Zheng were supported by NSF of China No.11831004. J. Zheng was also supported by PFCAEP project No. YZJJLX2019012. The authors are also grateful to Professor Shaoming Guo for his valuable discussion.

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Authors and Affiliations

  1. The Graduate School of China Academy of Engineering Physics, P. O. Box 2101, Beijing, 100088, China

    Zhuoran Li

  2. Institute of Applied Physics and Computational Mathematics, Beijing, 100088, China

    Changxing Miao & Jiqiang Zheng

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  1. Zhuoran Li
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  2. Changxing Miao
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  3. Jiqiang Zheng
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Correspondence to Jiqiang Zheng.

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Communicated by Eric Todd Quinto.

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Li, Z., Miao, C. & Zheng, J. A Restriction Estimate for a Certain Surface of Finite Type in \({\mathbb {R}}^3\). J Fourier Anal Appl 27, 63 (2021). https://doi.org/10.1007/s00041-021-09868-5

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  • DOI: https://doi.org/10.1007/s00041-021-09868-5

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