Previous |  Up |  Next


Title: The Brascamp–Lieb inequalities: recent developments (English)
Author: Carbery, Anthony
Language: English
Journal: Nonlinear Analysis, Function Spaces and Applications
Volume: Vol. 8
Issue: 2006
Pages: 9-34
Category: math
Summary: We discuss recent progress on issues surrounding the Brascamp–Lieb inequalities. (English)
Keyword: Brascamp–Lieb inequalities
MSC: 26-02
MSC: 26D15
MSC: 42B25
Date available: 2009-10-08T09:51:34Z
Last updated: 2013-10-18
Stable URL:
Reference: [Ball] 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). Zbl 0674.46008, MR 1008726
Reference: [Bar] 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. Zbl 0901.26010, MR 1650312, 10.1007/s002220050267
Reference: [Be] Beckner W.: Inequalities in Fourier analysis.Ann. Math. (2) 102 (1975), no. 1, 159–182. Zbl 0338.42017, MR 52 #6317. Zbl 0338.42017, MR 0385456, 10.2307/1970980
Reference: [BCCT1] Bennett J. M., Carbery A., Christ M., Tao T.: The Brascamp–Lieb inequalities: finiteness, structure and extremals.To appear in Geom. Funct. Anal. Zbl 1132.26006, MR 2377493
Reference: [BCCT2] 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
Reference: [BCT] 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. MR 2275834, 10.1007/s11511-006-0006-4
Reference: [BL] 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. Zbl 0339.26020, MR 0412366, 10.1016/0001-8708(76)90184-5
Reference: [BLL] 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. Zbl 0286.26005, MR 0346109, 10.1016/0022-1236(74)90013-5
Reference: [C] Calderón A. P.: An inequality for integrals.Studia Math. 57 (1976), no. 3, 275–277. Zbl 0343.26017, MR 54 #10531. Zbl 0343.26017, MR 0422544
Reference: [CLL] Carlen E. A., Lieb E. H., Loss M.: A sharp analog of Young’s inequality on $S^N$ and related entropy inequalities.J. Geom. Anal. 14 (2004), no. 3,487–520. Zbl 1056.43002, MR 2005k:82046. MR 2077162, 10.1007/BF02922101
Reference: [F] 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. Zbl 0761.60013, MR 1188047, 10.1214/aop/1176989534
Reference: [L] Lieb E. H.: Gaussian kernels have only Gaussian maximizers.Invent. Math. 102 (1990), no. 1, 179–208. Zbl 0726.42005, MR 91i:42014. Zbl 0726.42005, MR 1069246, 10.1007/BF01233426
Reference: [LW] 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. Zbl 0035.38302, MR 0031538, 10.1090/S0002-9904-1949-09320-5
Reference: [V1] Valdimarsson S. I.: Two geometric inequalities.Ph.D. Thesis, University of Edinburgh, 2006.
Reference: [V2] Valdimarsson S. I.: Optimisers for the Brascamp–Lieb inequality.Preprint. Zbl 1159.26007, MR 2448061


Files Size Format View
NAFSA_106-2006-1_3.pdf 427.7Kb application/pdf View/Open
Back to standard record
Partner of
EuDML logo