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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Restriction estimates for hyperbolic cone in high dimensions
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by Zhong Gao and Jiqiang Zheng
Proc. Amer. Math. Soc. 151 (2023), 1963-1977
DOI: https://doi.org/10.1090/proc/16259
Published electronically: February 28, 2023

Abstract:

In this paper, we obtain the $L^p$ restriction estimates for the truncated conic surface \begin{equation*} \Sigma =\big \{(\xi ’,\xi _n,-\xi _n^{-1}\langle \xi ’,N\xi ’\rangle ): (\xi ’,\xi _n)\in B^{n-1}(0,1)\times [1,2]\big \} \end{equation*} with $N=I_{n-1-m}\oplus (-I_m)$ for $m\leq \lfloor \tfrac {n-3}2\rfloor$ provided $p>\tfrac {2(n+3)}{n+1}$. The main ingredients of the proof are the bilinear estimates of strongly separated property and a geometric distribution about caps.
References
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Bibliographic Information
  • Zhong Gao
  • Affiliation: The Graduate School of China Academy of Engineering Physics, P.O. Box 2101, Beijing 100088, People’s Republic of China
  • Email: gaozhong18@gscaep.ac.cn
  • Jiqiang Zheng
  • Affiliation: Institute of Applied Physics and Computational Mathematics, P.O. Box 8009, Beijing 100088, People’s Republic of China
  • MR Author ID: 903431
  • Email: zhengjiqiang@gmail.com
  • Received by editor(s): April 29, 2022
  • Published electronically: February 28, 2023
  • Additional Notes: The second author is the corresponding author.
  • Communicated by: Ariel Barton
  • © Copyright 2023 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 151 (2023), 1963-1977
  • MSC (2020): Primary 42B10
  • DOI: https://doi.org/10.1090/proc/16259
  • MathSciNet review: 4556192