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Remarks on Wolff's inequality for hypersurfaces

  • SHAOMING GUO (a1) and CHANGKEUN OH (a2)

Abstract

We run an iteration argument due to Pramanik and Seeger, to provide a proof of sharp decoupling inequalities for conical surfaces and for k-cones. These are extensions of results of Łaba and Pramanik to sharp exponents.

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References

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[1] Bourgain, J. and Demeter, C. The proof of the l 2 decoupling conjecture. Ann. of Math. 182 (2015), no. 1, 351389.
[2] Bourgain, J. and Demeter, C. Decouplings for curves and hypersurfaces with nonzero Gaussian curvature. J. Anal. Math. 133 (1) (2017), 279311.
[3] Garrigós, G. and Seeger, A. On plate decompositions of cone multipliers. Proc. Edinb. Math. Soc. 52 (2009), no. 3, 631651.
[4] Garrigós, G. and Seeger, A. A mixed norm variant of Wolff's inequality for paraboloids. Harmonic analysis and partial differential equations. Contemp. Math. 505 (Amer. Math. Soc., Providence, RI, 2010), 179197.
[5] Łaba, I. and Pramanik, M. Wolff's inequality for hypersurfaces. Collect. Math. Exta(Vol. Extra) (2006), 293326.
[6] Łaba, I. and Wolff, T. A local smoothing estimate in higher dimensions. J. Anal. Math. 88 (2002), 149171.
[7] Pramanik, M. and Seeger, A. Lp regularity of averages over curves and bounds for associated maximal operators. Amer. J. Math. 129 (2007), no. 1, 61103.
[8] Wolff, T. Local smoothing type estimates on Lp for large p. Geom. Funct. Anal. 10 (2000), no. 5, 12371288.
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Mathematical Proceedings of the Cambridge Philosophical Society
  • ISSN: 0305-0041
  • EISSN: 1469-8064
  • URL: /core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society
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