A decoupling for Cantor-like sets
Author:
Ciprian Demeter
Journal:
Proc. Amer. Math. Soc. 147 (2019), 1037-1050
MSC (2010):
Primary 42A16; Secondary 52C99
DOI:
https://doi.org/10.1090/proc/14325
Published electronically:
December 6, 2018
MathSciNet review:
3896054
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Abstract | References | Similar Articles | Additional Information
Abstract: We consider partitions of the parabola determined by Cantor-like sets and prove decouplings in the range $2\le p\le 6$ that are independent of the parameters defining these sets.
- Enrico Bombieri and Jean Bourgain, A problem on sums of two squares, Int. Math. Res. Not. IMRN 11 (2015), 3343ā3407. MR 3373053, DOI https://doi.org/10.1093/imrn/rnu005
- Jean Bourgain and Ciprian Demeter, The proof of the $l^2$ decoupling conjecture, Ann. of Math. (2) 182 (2015), no. 1, 351ā389. MR 3374964, DOI https://doi.org/10.4007/annals.2015.182.1.9
- Jean Bourgain and Ciprian Demeter, A study guide for the $l^2$ decoupling theorem, Chin. Ann. Math. Ser. B 38 (2017), no. 1, 173ā200. MR 3592159, DOI https://doi.org/10.1007/s11401-016-1066-1
- Kathryn E. Hare and Ivo Klemes, On permutations of lacunary intervals, Trans. Amer. Math. Soc. 347 (1995), no. 10, 4105ā4127. MR 1308014, DOI https://doi.org/10.1090/S0002-9947-1995-1308014-7
- Manjunath Krishnapur, PƤr Kurlberg, and Igor Wigman, Nodal length fluctuations for arithmetic random waves, Ann. of Math. (2) 177 (2013), no. 2, 699ā737. MR 3010810, DOI https://doi.org/10.4007/annals.2013.177.2.8
- Terence Tao and Van Vu, Additive combinatorics, Cambridge Studies in Advanced Mathematics, vol. 105, Cambridge University Press, Cambridge, 2006. MR 2289012
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Additional Information
Ciprian Demeter
Affiliation:
Department of Mathematics, Indiana University, Bloomington, Indiana 47405
MR Author ID:
734783
Email:
demeterc@@indiana.edu
Keywords:
Discrete restriction estimates,
Cantor sets,
additive energy
Received by editor(s):
June 25, 2017
Published electronically:
December 6, 2018
Additional Notes:
The author was partially supported by the NSF Grant DMS-1161752.
Communicated by:
Alexander Iosevich
Article copyright:
© Copyright 2018
American Mathematical Society
