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A sharp L10 decoupling for the twisted cubic

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Abstract

We prove a sharp l10(L10) decoupling for the moment curve in ℝ3. The proof involves a two-step decoupling combined with new incidence estimates for planks, tubes and plates.

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References

  1. J. Bennett, A. Carbery and T. Tao, On the multilinear restriction and Kakeya conjectures, Acta Math. 196 (2006), 261–302.

    Article  MathSciNet  MATH  Google Scholar 

  2. J. Bourgain, Decoupling inequalities and some mean-value theorems, J. Anal. Math. 133 (2017), 313–334.

    Article  MathSciNet  MATH  Google Scholar 

  3. J. Bourgain, Decoupling, exponential sums and the Riemann zeta function, J. Amer. Math. Soc. 30 (2017), 205–224.

    Article  MathSciNet  MATH  Google Scholar 

  4. J. Bourgain and C. Demeter, The proof of the l2decoupling conjecture, Ann. of Math. (2) 182 (2015), 351–389.

    Article  MathSciNet  MATH  Google Scholar 

  5. J. Bourgain and C. Demeter, Decouplings for surfaces in ℝ4, J. Funct. Anal. 270 (2016), 1299–1318.

    Article  MathSciNet  MATH  Google Scholar 

  6. J. Bourgain and C. Demeter, Decouplings for curves and hypersurfaces with nonzero Gaussian curvature, J. Anal. Math. 133 (2017), 279–311.

    Article  MathSciNet  MATH  Google Scholar 

  7. J. Bourgain, C. Demeter and L. Guth, Proof of the main conjecture in Vinogradov’s mean value theorem for degrees higher than three, Ann. of Math. (2) 184 (2016), 633–682.

    Article  MathSciNet  MATH  Google Scholar 

  8. J. Bourgain and L. Guth, Bounds on oscillatory integral operators based on multilinear estimates, Geom. Funct. Anal. 21 (2011), 1239–1295.

    Article  MathSciNet  MATH  Google Scholar 

  9. L. Brandolini, G. Gigante, A. Greenleaf, A. Iosevich, A. Seeger and G. Travaglini, Average decay estimates for Fourier transforms of measures supported on curves, J. Geom. Anal. 17 (2007), 15–40.

    Article  MathSciNet  MATH  Google Scholar 

  10. C. Demeter, Fourier Restriction, Decoupling and Applications, Cambridge University Press, Cambridge, 2020.

    Book  MATH  Google Scholar 

  11. C. Demeter, private communication.

  12. C. Demeter and S. Guo, unpublished work.

  13. C. Demeter, S. Guo and F. Shi, Sharp decouplings for three dimensional manifolds in ℝ5, Rev. Mat. Iberoam. 35 (2019), 423–460.

    Article  MathSciNet  MATH  Google Scholar 

  14. C. Demeter, L. Guth and H. Wang, Small cap decouplings, Geom. Funct. Anal. 30 (2020), 989–1062.

    Article  MathSciNet  MATH  Google Scholar 

  15. S. W. Drury, Restrictions of Fourier transforms to curves, Ann. Inst. Fourier (Grenoble) 35 (1985), 117–123.

    Article  MathSciNet  MATH  Google Scholar 

  16. L. Guth, N. Solomon and H. Wang, Incidence estimates for well spaced tubes, Geom. Funct. Anal. 29 (2019), 1844–1863.

    Article  MathSciNet  MATH  Google Scholar 

  17. L. Guth, H. Wang and R. Zhang, A sharp square function estimate for the cone in ℝ3, Ann. of Math. (2) 192 (2020), 551–581.

    Article  MathSciNet  MATH  Google Scholar 

  18. C. Oh, Small cap decoupling inequalities: bilinear methods, Rev. Mat. Iberoam. 38 (2022), 33–52.

    Article  MathSciNet  MATH  Google Scholar 

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Acknowledgment

I would like to thank my advisor Ciprian Demeter for his guidance and constant support throughout the completion of the project. I would also like to thank the anonymous referee for insightful comments and suggestions that have led to the simplification of Sections 3 and 4 of this paper.

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Authors and Affiliations

  1. Department of Mathematics, Indiana University, Bloomington, IN, 47405-7000, USA

    Hongki Jung

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  1. Hongki Jung
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Correspondence to Hongki Jung.

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Jung, H. A sharp L10 decoupling for the twisted cubic. JAMA 149, 563–609 (2023). https://doi.org/10.1007/s11854-022-0258-8

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  • DOI: https://doi.org/10.1007/s11854-022-0258-8

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