The Brascamp–Lieb inequalities: recent developments
Carbery, Anthony
Nonlinear Analysis, Function Spaces and Applications, GDML_Books, (2007), p. 9-34 / Harvested from
Access to full text
Full (PDF)

We discuss recent progress on issues surrounding the Brascamp–Lieb inequalities.

EUDML-ID : urn:eudml:doc:221044
Mots clés:
Mots clés: 
@article{702493,
     title = {The Brascamp--Lieb inequalities: recent developments},
     booktitle = {Nonlinear Analysis, Function Spaces and Applications},
     series = {GDML\_Books},
     publisher = {Institute of Mathematics of the Academy of Sciences of the Czech Republic},
     address = {Praha},
     year = {2007},
     pages = {9-34},
     url = {http://dml.mathdoc.fr/item/702493}
}

Carbery, Anthony. The Brascamp–Lieb inequalities: recent developments, dans Nonlinear Analysis, Function Spaces and Applications, GDML_Books,  (2007), pp. 9-34. http://gdmltest.u-ga.fr/item/702493/

Bennett J. M.; Carbery A.; Christ M.; Tao T. The Brascamp–Lieb inequalities: finiteness, structure and extremals, To appear in Geom. Funct. Anal. | MR 2377493 | Zbl 1132.26006

Bennett J. M.; Carbery A.; Christ M.; Tao T. Finite bounds for Hölder–Brascamp–Lieb multilinear inequalities, To appear in Math. Res. Lett. | MR 2661170

Carlen E. A.; Lieb E. H.; Loss M. A sharp analog of Young’s inequality on SN and related entropy inequalities, J. Geom. Anal. 14 (2004), no. 3,487–520. Zbl 1056.43002, MR 2005k:82046. | MR 2077162

Valdimarsson S. I. Two geometric inequalities, Ph.D. Thesis, University of Edinburgh, 2006.

Valdimarsson S. I. Optimisers for the Brascamp–Lieb inequality, Preprint. | MR 2448061 | Zbl 1159.26007

Loomis L. H.; Whitney H. An inequality related to the isoperimetric inequality, Bull. Amer. Math. Soc. 55 (1949), 961–962. Zbl 0035.38302, MR 11,166d. (1949) | MR 0031538 | Zbl 0035.38302

Bennett J. M.; Carbery A.; Tao T. On the multilinear restriction and Kakeya conjectures, Acta Math. 196 (2006), no. 2, 261–302. Zbl pre05114945, MR 2007h:42019. (196 ) | MR 2275834

Brascamp H. J.; Lieb E. H.; Luttinger J. M. A general rearrangement inequality for multiple integrals, J. Funct. Anal. 17 (1974), 227–237. Zbl 0286.26005, MR 49 #10835. (1974) | MR 0346109 | Zbl 0286.26005

Beckner W. Inequalities in Fourier analysis, Ann. Math. (2) 102 (1975), no. 1, 159–182. Zbl 0338.42017, MR 52 #6317. (1975) | MR 0385456 | Zbl 0338.42017

Brascamp H. J.; Lieb E. H. Best constants in Young’s inequality, its converse, and its generalization to more than three functions, Adv. Math. 20 (1976), no. 2, 151–173. Zbl 0339.26020, MR 54 #492. (1976) | MR 0412366 | Zbl 0339.26020

Calderón A. P. An inequality for integrals, Studia Math. 57 (1976), no. 3, 275–277. Zbl 0343.26017, MR 54 #10531. (1976) | MR 0422544 | Zbl 0343.26017

Ball K. M. Volumes of sections of cubes and related problems, Geometric aspects of functional analysis (J. Lindenstrauss and V. D. Milman, eds.), Lecture Notes in Math. 1376, Springer, Heidelberg, 1989, pp. 251–260. Zbl 0674.46008, MR1008726 (90i:52019). (1989) | MR 1008726 | Zbl 0674.46008

Lieb E. H. Gaussian kernels have only Gaussian maximizers, Invent. Math. 102 (1990), no. 1, 179–208. Zbl 0726.42005, MR 91i:42014. (1990) | MR 1069246 | Zbl 0726.42005

Finner H. A generalization of Hölder’s inequality and some probability inequalities, Ann. Probab. 20 (1992), no. 4, 1893–1901. Zbl 0761.60013, MR 93k:60047. (1992) | MR 1188047 | Zbl 0761.60013

Barthe F. On a reverse form of the Brascamp–Lieb inequality, Invent. Math. 134 (1998), no. 2, 335–361. Zbl 0901.26010, MR 99i:26021. (1998) | MR 1650312 | Zbl 0901.26010