Geometric Brascamp–Lieb Has the Optimal Best Constant
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Abstract
We study the optimal best constant for the Brascamp–Lieb inequality and show that it is furnished exactly by the geometric Brascamp–Lieb inequality.
Keywords
Brascamp–Lieb inequality Optimal best constant MinimaxMathematics Subject Classification (2000)
44A35 49Q20 42B99Preview
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References
- 1.Ball, K.: Volumes of sections of cubes and related problems. In: Geometric Aspects of Functional Analysis (1987–1988). Lecture Notes in Math., vol. 1376, pp. 251–260. Springer, Berlin (1989). MR MR1008726 (90i:52019) CrossRefGoogle Scholar
- 2.Barthe, F.: On a reverse form of the Brascamp–Lieb inequality. Invent. Math. 134(2), 335–361 (1998). MR MR1650312 (99i:26021) MathSciNetCrossRefGoogle Scholar
- 3.Bennett, J., Carbery, A., Christ, M., Tao, T.: The Brascamp–Lieb inequalities: finiteness, structure, and extremals. Geom. Funct. Anal. (to appear). doi: 10.1007/s00039-007-0619-6
- 4.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(2), 151–173 (1976). MR MR0412366 (54 #492) MathSciNetzbMATHCrossRefGoogle Scholar
- 5.Carlen, E.A., Cordero–Erausquin, D.: Subadditivity of the entropy and its relation to Brascamp-Lieb type inequalities (2007). doi: 10.1007/s00039-009-0001-y
- 6.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(3), 487–520 (2004). MR MR2077162 (2005k:82046) MathSciNetzbMATHGoogle Scholar
- 7.Lieb, E.H.: Gaussian kernels have only Gaussian maximizers. Invent. Math. 102(1), 179–208 (1990). MR MR1069246 (91i:42014) MathSciNetzbMATHCrossRefGoogle Scholar
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