This service is more advanced with JavaScript available, learn more at http://activatejavascript.org

Journal of Geometric Analysis

October 2011, Volume 21, Issue 4, pp 1036–1043

Geometric Brascamp–Lieb Has the Optimal Best Constant

Authors
Authors and affiliations

Stefán Ingi ValdimarssonEmail author

Article

First Online:: 10 September 2010

Received:: 28 September 2009

1 Citations

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 Minimax

Mathematics Subject Classification (2000)

44A35 49Q20 42B99

Preview

Unable to display preview. Download preview PDF.

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) MathSciNetMATHCrossRefGoogle 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) MathSciNetMATHGoogle Scholar
7.
Lieb, E.H.: Gaussian kernels have only Gaussian maximizers. Invent. Math. 102(1), 179–208 (1990). MR MR1069246 (91i:42014) MathSciNetMATHCrossRefGoogle Scholar

Copyright information

© Mathematica Josephina, Inc. 2010

Authors and Affiliations

Stefán Ingi Valdimarsson
- 1
Email author

1.Science InstituteUniversity of IcelandReykjavikIceland

Personalised recommendations

Actions

Unlimited access to the full article
Instant download
Include local sales tax if applicable

Subscribe to Journal

Get Access to

Journal of Geometric Analysis

for the whole of 2017

Export citation