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A study guide for the l 2 decoupling theorem


This paper contains a detailed, self contained and more streamlined proof of the l 2 decoupling theorem for hypersurfaces from the paper of Bourgain and Demeter in 2015. The authors hope this will serve as a good warm up for the readers interested in understanding the proof of Vinogradov’s mean value theorem from the paper of Bourgain, Demeter and Guth in 2015.

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The authors are grateful to Zane Li and Terry Tao for pointing out a few inaccuracies in an earlier version of this manuscript.

Author information

Correspondence to Jean Bourgain.

Additional information

Dedicated to Haim Brezis on the occasion of his 70th birthday

This work was supported by the NSF Grant DMS-1301619 and the NSF Grant DMS-1161752.

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Bourgain, J., Demeter, C. A study guide for the l 2 decoupling theorem. Chin. Ann. Math. Ser. B 38, 173–200 (2017).

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  • Restriction theorems
  • Multilinear Kakeya inequality
  • Decouplings

2000 MR Subject Classification

  • 42B37