Hostname: page-component-586b7cd67f-l7hp2 Total loading time: 0 Render date: 2024-12-01T03:10:26.378Z Has data issue: false hasContentIssue false

Remarks on Wolff's inequality for hypersurfaces

Published online by Cambridge University Press:  06 September 2018

SHAOMING GUO
Affiliation:
Department of Mathematics, Indiana University, 831 East 3rd St., Bloomington IN 47405, U.S.A. e-mail: [email protected]
CHANGKEUN OH
Affiliation:
Department of Mathematics, Pohang University of Science and Technology, Pohang 790-784, Republic of Korea. e-mail: [email protected]

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.

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 2018 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[1] Bourgain, J. and Demeter, C. The proof of the l 2 decoupling conjecture. Ann. of Math. 182 (2015), no. 1, 351389.Google Scholar
[2] Bourgain, J. and Demeter, C. Decouplings for curves and hypersurfaces with nonzero Gaussian curvature. J. Anal. Math. 133 (1) (2017), 279311.Google Scholar
[3] Garrigós, G. and Seeger, A. On plate decompositions of cone multipliers. Proc. Edinb. Math. Soc. 52 (2009), no. 3, 631651.Google Scholar
[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.Google Scholar
[5] Łaba, I. and Pramanik, M. Wolff's inequality for hypersurfaces. Collect. Math. Exta(Vol. Extra) (2006), 293326.Google Scholar
[6] Łaba, I. and Wolff, T. A local smoothing estimate in higher dimensions. J. Anal. Math. 88 (2002), 149171.Google Scholar
[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.Google Scholar
[8] Wolff, T. Local smoothing type estimates on Lp for large p. Geom. Funct. Anal. 10 (2000), no. 5, 12371288.Google Scholar