Hostname: page-component-784d4fb959-xqrh7 Total loading time: 0 Render date: 2025-07-16T11:45:05.601Z Has data issue: false hasContentIssue false
  • English
  • Français

A short proof of the multilinear Kakeya inequality

Published online by Cambridge University Press:  08 December 2014

LARRY GUTH
LARRY GUTH*
Affiliation:
Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA 02139, U.S.A. e-mail: larry.guth.work@gmail.com
Get access Rights & Permissions [Opens in a new window]

Abstract

We give a short proof of a slightly weaker version of the multilinear Kakeya inequality proven by Bennett, Carbery and Tao.

Information

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 158 , Issue 1 , January 2015 , pp. 147 - 153
Copyright
Copyright © Cambridge Philosophical Society 2014 

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.)

Article purchase

Temporarily unavailable

References

REFERENCES

[B]Bourgain, J.Moment inequalities for trigonometric polynomials with spectrum in curved hypersurfaces. Israel J. Math. 193 (2013), no. 1, 441–458.CrossRefGoogle Scholar
[BB]Bennett, J. and Bez, N.Some nonlinear Brascamp–Lieb inequalities and applications to harmonic analysis. J. Funct. Anal. 259 (2010), no. 10, 2520–2556.Google Scholar
[BHT]Bejenaru, I., Herr, S. and Tataru, D.A convolution estimate for two-dimensional hypersurfaces. Rev. Mat. Iberoam. 26 (2010), no. 2, 707–728.Google Scholar
[BD]Bourgain, J. and Demeter, C. The proof of the l 2 decoupling conjecture. arXiv:1403.5335.Google Scholar
[BG]Bourgain, J. and Guth, L.Bounds on oscillatory integral operators based on multilinear estimates. Geom. Funct. Anal. 21 (2011), no. 6, 1239–1295.CrossRefGoogle Scholar
[BCT]Bennett, J., Carbery, A. and Tao, T.On the multilinear restriction and Kakeya conjectures. Acta Math. 196 (2006), no. 2, 261–302.Google Scholar
[CJ]Csőrnyei, M. and Jones, P. Product Formulas for measures and applications to analysis and geometry. URL: www.math.sunysb.edu/Videos/dfest/PDFs/38-Jones.pdfGoogle Scholar
[G]Guth, L.The endpoint case of the Bennett–Carbery–Tao multilinear Kakeya conjecture. Acta Math. 205 (2010), no. 2, 263–286.CrossRefGoogle Scholar
[LW]Loomis, L. and Whitney, H.An inequality related to the isoperimetric inequality. Bull. Amer. Math. Soc 55 (1949), 961–962.Google Scholar
[S]Stein, E.Some problems in harmonic analysis. Harmonic analysis in Euclidean spaces. Proc. Symp. Pure Math. (Williams Coll., Williamstown, Mass., 1978), Part 1, pp. 3–20; Proc. Symp. Pure Math., XXXV, Part 2 (Amer. Math. Soc., Providence, R.I., 1979).Google Scholar