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A Sobolev estimate for the adjoint restriction operator

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In this note we consider the adjoint restriction estimate for hypersurface under additional regularity assumption. We obtain the optimal \(H^s\)-\(L^q\) estimates and their mixed norm generalizations. As applications we prove some weighted Strichartz estimates for the propagator \(\varphi \rightarrow e^{it(-\Delta )^{ \alpha / 2}}\varphi \), \(\alpha >0\).

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Acknowledgments

Y. Cho is supported by NRF Grant 2011-0005122 (Republic of Korea). Z. Guo is supported in part by NNSF of China (No.11371037), Beijing Higher Education Young Elite Teacher Project (No. YETP0002), and Fok Ying Tong education foundation (No. 141003) and ARC Discovery Grant DP110102488. S. Lee is supported in part by NRF Grant 2012008373 (Republic of Korea). The second named author would like to thank J. Bourgain for a discussion about the restriction estimate and his encouragement.

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Authors and Affiliations

  1. Department of Mathematics, Institute of Pure and Applied Mathematics, Chonbuk National University, Jeonju, 561-756, Republic of Korea

    Yonggeun Cho

  2. School of Mathematical Sciences, Peking University, Beijing, 100871, China

    Zihua Guo

  3. Department of Mathematical Sciences, Seoul National University, Seoul, 151-747, Republic of Korea

    Sanghyuk Lee

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  1. Yonggeun Cho
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  2. Zihua Guo
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  3. Sanghyuk Lee
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Correspondence to Zihua Guo.

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Cho, Y., Guo, Z. & Lee, S. A Sobolev estimate for the adjoint restriction operator. Math. Ann. 362, 799–815 (2015). https://doi.org/10.1007/s00208-014-1130-7

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  • DOI: https://doi.org/10.1007/s00208-014-1130-7

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