×
Zhang, Ruixiang

The endpoint perturbed Brascamp-Lieb inequalities with examples. (English) Zbl 1378.42008

Anal. PDE 11, No. 3, 555-581 (2018).
Summary: We prove the folklore endpoint multilinear \(k_{j}\)-plane conjecture originating in a paper of J. Bennett et al. [Acta Math. 196, No. 2, 261–302 (2006; Zbl 1203.42019)] where the almost sharp multilinear Kakeya estimate was proved. Along the way we prove a more general result, namely the endpoint multilinear \(k_{j}\)-variety theorem. Finally, we generalize our results to the endpoint perturbed Brascamp-Lieb inequalities using techniques in earlier sections.

Cited in 1 Review
Cited in 9 Documents

MSC:

42B10 Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type

Keywords:

Brascamp-Lieb inequality; polynomial method

Citations:

Zbl 1203.42019
PDF BibTeX XML Cite
\textit{R. Zhang}, Anal. PDE 11, No. 3, 555--581 (2018; Zbl 1378.42008)
Full Text: DOI arXiv
  • logo of hbz
  • logo of WorldCat

References:

[1] ; Bennett, Harmonic analysis and partial differential equations. Contemp. Math., 612, 1 (2014)
[2] 10.1016/j.jfa.2010.07.015 · Zbl 1213.26021
[3] 10.1007/s11511-006-0006-4 · Zbl 1203.42019
[4] 10.1007/s00039-007-0619-6 · Zbl 1132.26006
[5] 10.4310/MRL.2010.v17.n4.a6 · Zbl 1247.26029
[6] 10.1007/BF01896376 · Zbl 0756.42014
[7] 10.1007/s11856-012-0077-1 · Zbl 1271.42039
[8] 10.1134/S0081543813010045 · Zbl 1291.35253
[9] ; Bourgain, Ann. of Math. (2), 182, 351 (2015)
[10] 10.1007/s00039-011-0140-9 · Zbl 1237.42010
[11] 10.1007/s11511-010-0055-6 · Zbl 1210.52004
[12] 10.1017/S0305004114000589 · Zbl 1371.42007
[13] 10.4171/RMI/891 · Zbl 1358.52011
[14] ; Guth, J. Amer. Math. Soc., 29, 371 (2016)
[15] ; John, Studies and essays presented to R. Courant on his 60th birthday, January 8, 1948, 187 (1948)
[16] 10.1007/BF01233426 · Zbl 0726.42005
[17] 10.1512/iumj.1982.31.31046 · Zbl 0548.44003
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.