A study guide for the l 2 decoupling theorem

Jean Bourgain , Ciprian Demeter

Chinese Annals of Mathematics, Series B ›› 2017, Vol. 38 ›› Issue (1) : 173 -200.

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Chinese Annals of Mathematics, Series B ›› 2017, Vol. 38 ›› Issue (1) : 173 -200. DOI: 10.1007/s11401-016-1066-1
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A study guide for the l 2 decoupling theorem

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Abstract

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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Restriction theorems / Multilinear Kakeya inequality / Decouplings

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Jean Bourgain, Ciprian Demeter. A study guide for the l 2 decoupling theorem. Chinese Annals of Mathematics, Series B, 2017, 38(1): 173-200 DOI:10.1007/s11401-016-1066-1

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References

[1]

Bennett J., Carbery A., Tao T.. On the multilinear restriction and Kakeya conjectures. Acta Math., 2006, 196(2): 261-302

[2]

Bourgain J.. Moment inequalities for trigonometric polynomials with spectrum in curved hypersurfaces. Israel J. Math., 2013, 193(1): 441-458

[3]

Bourgain J., Demeter C.. The proof of the l2 decoupling conjecture. Annals of Math., 2015, 182(1): 351-389

[4]

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

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Bourgain J., Guth L.. Bounds on oscillatory integral operators based on multilinear estimates. Geom. Funct. Anal., 2011, 21(6): 1239-1295

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Guth L.. A short proof of the multilinear Kakeya inequality. Math. Proc. Cambridge Philos. Soc., 2015, 158(1): 147-153

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