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

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.

### MSC:

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

### Keywords:

Brascamp-Lieb inequality; polynomial method

Zbl 1203.42019
Full Text:

### 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
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