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Journal articles on the topic 'Brascamp-Lieb inequalities'

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Published: 9 March 2023

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1

Zorin-Kranich, Pavel. "Kakeya–Brascamp–Lieb inequalities." Collectanea Mathematica 71, no. 3 (2019): 471–92. http://dx.doi.org/10.1007/s13348-019-00273-2.

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2

Bennett, Jonathan, Neal Bez, and Susana Gutiérrez. "Global Nonlinear Brascamp–Lieb Inequalities." Journal of Geometric Analysis 23, no. 4 (2012): 1806–17. http://dx.doi.org/10.1007/s12220-012-9307-3.

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3

Duncan, Jennifer. "An Algebraic Brascamp–Lieb Inequality." Journal of Geometric Analysis 31, no. 10 (2021): 10136–63. http://dx.doi.org/10.1007/s12220-021-00638-9.

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AbstractThe Brascamp–Lieb inequalities are a very general class of classical multilinear inequalities, well-known examples of which being Hölder’s inequality, Young’s convolution inequality, and the Loomis–Whitney inequality. Conventionally, a Brascamp–Lieb inequality is defined as a multilinear Lebesgue bound on the product of the pullbacks of a collection of functions $$f_j\in L^{q_j}(\mathbb {R}^{n_j})$$ f j ∈ L q j ( R n j ) , for $$j=1,\ldots ,m$$ j = 1 , … , m , under some corresponding linear maps $$B_j$$ B j . This regime is now fairly well understood (Bennett et al. in Geom Funct Anal
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4

Arnaudon, Marc, Michel Bonnefont, and Aldéric Joulin. "Intertwinings and generalized Brascamp–Lieb inequalities." Revista Matemática Iberoamericana 34, no. 3 (2018): 1021–54. http://dx.doi.org/10.4171/rmi/1014.

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5

Iglesias, David, and Jesús Yepes Nicolás. "On discrete Borell–Brascamp–Lieb inequalities." Revista Matemática Iberoamericana 36, no. 3 (2019): 711–22. http://dx.doi.org/10.4171/rmi/1145.

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6

Bramati, Roberto. "Brascamp–Lieb Inequalities on Compact Homogeneous Spaces." Analysis and Geometry in Metric Spaces 7, no. 1 (2019): 130–57. http://dx.doi.org/10.1515/agms-2019-0007.

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Abstract We provide a general strategy to construct multilinear inequalities of Brascamp–Lieb type on compact homogeneous spaces of Lie groups. As an application we obtain sharp integral inequalities on the real unit sphere involving functions with some degree of symmetry.
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7

Durcik, Polona, and Christoph Thiele. "Singular Brascamp–Lieb inequalities with cubical structure." Bulletin of the London Mathematical Society 52, no. 2 (2020): 283–98. http://dx.doi.org/10.1112/blms.12310.

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8

O’Neill, Kevin. "A variation on Hölder–Brascamp–Lieb inequalities." Transactions of the American Mathematical Society 373, no. 8 (2020): 5467–89. http://dx.doi.org/10.1090/tran/8070.

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9

Carlen, Eric A., and Elliott H. Lieb. "Brascamp--Lieb inequalities for non-commutative integration." Documenta Mathematica 13 (2008): 553–84. http://dx.doi.org/10.4171/dm/254.

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10

Cordero-Erausquin, Dario. "Transport Inequalities for Log-concave Measures, Quantitative Forms, and Applications." Canadian Journal of Mathematics 69, no. 3 (2017): 481–501. http://dx.doi.org/10.4153/cjm-2016-046-3.

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AbstractWe review some simple techniques based on monotonemass transport that allow us to obtain transport-type inequalities for any log-concave probability measures, and formore generalmeasures as well. We discuss quantitative forms of these inequalities, with application to the Brascamp-Lieb variance inequality.
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11

Zhang, Ruixiang. "The endpoint perturbed Brascamp–Lieb inequalities with examples." Analysis & PDE 11, no. 3 (2018): 555–81. http://dx.doi.org/10.2140/apde.2018.11.555.

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12

Bennett, Jonathan, Anthony Carbery, Michael Christ, and Terence Tao. "The Brascamp–Lieb Inequalities: Finiteness, Structure and Extremals." Geometric and Functional Analysis 17, no. 5 (2007): 1343–415. http://dx.doi.org/10.1007/s00039-007-0619-6.

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13

Bennett, Jonathan, Anthony Carbery, Michael Christ, and Terence Tao. "Finite bounds for Hölder-Brascamp-Lieb multilinear inequalities." Mathematical Research Letters 17, no. 4 (2010): 647–66. http://dx.doi.org/10.4310/mrl.2010.v17.n4.a6.

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14

Balogh, Zoltán M., and Alexandru Kristály. "Equality in Borell–Brascamp–Lieb inequalities on curved spaces." Advances in Mathematics 339 (December 2018): 453–94. http://dx.doi.org/10.1016/j.aim.2018.09.041.

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15

Bacher, Kathrin. "On Borell-Brascamp-Lieb Inequalities on Metric Measure Spaces." Potential Analysis 33, no. 1 (2009): 1–15. http://dx.doi.org/10.1007/s11118-009-9157-1.

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16

Bolley, François, Dario Cordero-Erausquin, Yasuhiro Fujita, Ivan Gentil, and Arnaud Guillin. "New Sharp Gagliardo–Nirenberg–Sobolev Inequalities and an Improved Borell–Brascamp–Lieb Inequality." International Mathematics Research Notices 2020, no. 10 (2018): 3042–83. http://dx.doi.org/10.1093/imrn/rny111.

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Abstract We propose a new Borell–Brascamp–Lieb inequality that leads to novel sharp Euclidean inequalities such as Gagliardo–Nirenberg–Sobolev inequalities in $ {\mathbb{R}}^n$ and in the half-space $ {\mathbb{R}}^n_+$. This gives a new bridge between the geometric point of view of the Brunn–Minkowski inequality and the functional point of view of the Sobolev-type inequalities. In this way we unify, simplify, and generalize results by S. Bobkov–M. Ledoux, M. del Pino–J. Dolbeault, and B. Nazaret.
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17

Koch, Herbert, and Stefan Steinerberger. "Convolution estimates for singular measures and some global nonlinear Brascamp—Lieb inequalities." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 145, no. 6 (2015): 1223–37. http://dx.doi.org/10.1017/s0308210515000323.

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We give an L2 x L2 → L2 convolution estimate for singular measures supported on transversal hypersurfaces in ℝn, which improves earlier results of Bejenaru et al. as well as Bejenaru and Herr. The quantities arising are relevant to the study of the validity of bilinear estimates for dispersive partial differential equations. We also prove a class of global, nonlinear Brascamp–Lieb inequalities with explicit constants in the same spirit.
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18

Liu, Jingbo, Thomas A. Courtade, Paul Cuff, and Sergio Verdu. "Smoothing Brascamp-Lieb Inequalities and Strong Converses of Coding Theorems." IEEE Transactions on Information Theory 66, no. 2 (2020): 704–21. http://dx.doi.org/10.1109/tit.2019.2953151.

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19

Kolesnikov, Alexander V., and Emanuel Milman. "Brascamp–Lieb-Type Inequalities on Weighted Riemannian Manifolds with Boundary." Journal of Geometric Analysis 27, no. 2 (2016): 1680–702. http://dx.doi.org/10.1007/s12220-016-9736-5.

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20

M�ndez-Hern�ndez, Pedro J. "Brascamp-Lieb-Luttinger inequalities for convex domains of finite inradius." Duke Mathematical Journal 113, no. 1 (2002): 93–131. http://dx.doi.org/10.1215/s0012-7094-02-11313-1.

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21

Bennett, Jonathan, and Neal Bez. "Some nonlinear Brascamp–Lieb inequalities and applications to harmonic analysis." Journal of Functional Analysis 259, no. 10 (2010): 2520–56. http://dx.doi.org/10.1016/j.jfa.2010.07.015.

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22

Bolley, François, Ivan Gentil, and Arnaud Guillin. "Dimensional improvements of the logarithmic Sobolev, Talagrand and Brascamp–Lieb inequalities." Annals of Probability 46, no. 1 (2018): 261–301. http://dx.doi.org/10.1214/17-aop1184.

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23

Bobkov, S. G., and M. Ledoux. "From Brunn-Minkowski to Brascamp-Lieb and to logarithmic Sobolev inequalities." Geometric and Functional Analysis 10, no. 5 (2000): 1028–52. http://dx.doi.org/10.1007/pl00001645.

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24

Garg, Ankit, Leonid Gurvits, Rafael Oliveira, and Avi Wigderson. "Algorithmic and optimization aspects of Brascamp-Lieb inequalities, via Operator Scaling." Geometric and Functional Analysis 28, no. 1 (2018): 100–145. http://dx.doi.org/10.1007/s00039-018-0434-2.

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25

Huang, Guangyue, and Mingfang Zhu. "Some geometric inequalities on Riemannian manifolds associated with the generalized modified Ricci curvature." Journal of Mathematical Physics 63, no. 11 (2022): 111508. http://dx.doi.org/10.1063/5.0116994.

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In this paper, by establishing a Reilly-type formula with respect to the ϕ-Laplacian associated with the generalized modified Ricci curvature, we first obtain sharp lower bound estimates for the first eigenvalue of the ϕ-Laplacian. On the other hand, some new Brascamp–Lieb-type and Colesanti-type inequalities under some suitable boundary conditions are achieved. As applications, we also obtain some relationships between the weighted mean curvature of a boundary submanifold and the mean curvature of submanifold x : ∂M → R N( K) into space form R N( K).
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26

Bennett, Jonathan, and Neal Bez. "Generating monotone quantities for the heat equation." Journal für die reine und angewandte Mathematik (Crelles Journal) 2019, no. 756 (2019): 37–63. http://dx.doi.org/10.1515/crelle-2017-0025.

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AbstractThe purpose of this article is to expose and further develop a simple yet surprisingly far-reaching framework for generating monotone quantities for positive solutions to linear heat equations in euclidean space. This framework is intimately connected to the existence of a rich variety of algebraic closure properties of families of sub/super-solutions, and more generally solutions of systems of differential inequalities capturing log-convexity properties such as the Li–Yau gradient estimate. Various applications are discussed, including connections with the general Brascamp–Lieb inequa
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27

Barman, Kalyan, and Neelesh S. Upadhye. "On Brascamp–Lieb and Poincaré type inequalities for generalized tempered stable distribution." Statistics & Probability Letters 189 (October 2022): 109600. http://dx.doi.org/10.1016/j.spl.2022.109600.

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28

Funaki, Tadahisa, and Kou Toukairin. "Dynamic approach to a stochastic domination: The FKG and Brascamp-Lieb inequalities." Proceedings of the American Mathematical Society 135, no. 6 (2007): 1915–22. http://dx.doi.org/10.1090/s0002-9939-07-08757-6.

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29

Cordero-Erausquin, Dario. "On matrix-valued log-concavity and related Prékopa and Brascamp-Lieb inequalities." Advances in Mathematics 351 (July 2019): 96–116. http://dx.doi.org/10.1016/j.aim.2019.04.046.

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30

Carlen, Eric A., and Dario Cordero–Erausquin. "Subadditivity of The Entropy and its Relation to Brascamp–Lieb Type Inequalities." Geometric and Functional Analysis 19, no. 2 (2009): 373–405. http://dx.doi.org/10.1007/s00039-009-0001-y.

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31

Lanconelli, Alberto. "A new approach to Poincaré-type inequalities on the Wiener space." Stochastics and Dynamics 16, no. 01 (2015): 1650002. http://dx.doi.org/10.1142/s0219493716500027.

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We prove a new type of Poincaré inequality on abstract Wiener spaces for a family of probability measures that are absolutely continuous with respect to the reference Gaussian measure. This class of probability measures is characterized by the strong positivity (a notion introduced by Nualart and Zakai in [22]) of their Radon–Nikodym densities. In general, measures of this type do not belong to the class of log-concave measures, which are a wide class of measures satisfying the Poincaré inequality (Brascamp and Lieb [2]). Our approach is based on a pointwise identity relating Wick and ordinary
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32

Alonso-Gutiérrez, David. "VOLUME ESTIMATES FOR L p ‐ZONOTOPES AND BEST BEST CONSTANTS IN BRASCAMP–LIEB INEQUALITIES." Mathematika 56, no. 1 (2009): 45–60. http://dx.doi.org/10.1112/s0025579309000345.

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33

Carlen, Eric A., Dario Cordero-Erausquin, and Elliott H. Lieb. "Asymmetric covariance estimates of Brascamp–Lieb type and related inequalities for log-concave measures." Annales de l'Institut Henri Poincaré, Probabilités et Statistiques 49, no. 1 (2013): 1–12. http://dx.doi.org/10.1214/11-aihp462.

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34

Helffer, Bernard. "Remarks on Decay of Correlations and Witten Laplacians Brascamp–Lieb Inequalities and Semiclassical Limit." Journal of Functional Analysis 155, no. 2 (1998): 571–86. http://dx.doi.org/10.1006/jfan.1997.3239.

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35

Nguyen, Van Hoang. "Dimensional variance inequalities of Brascamp–Lieb type and a local approach to dimensional Prékopaʼs theorem". Journal of Functional Analysis 266, № 2 (2014): 931–55. http://dx.doi.org/10.1016/j.jfa.2013.11.003.

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36

Christ, Michael, and Taryn C. Flock. "Cases of equality in certain multilinear inequalities of Hardy–Riesz–Rogers–Brascamp–Lieb–Luttinger type." Journal of Functional Analysis 267, no. 4 (2014): 998–1010. http://dx.doi.org/10.1016/j.jfa.2014.03.005.

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37

Maldague, Dominique. "Regularized Brascamp–lieb Inequalities And An Application." Quarterly Journal of Mathematics, July 15, 2021. http://dx.doi.org/10.1093/qmath/haab032.

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Abstract We present a certain regularized version of Brascamp–Lieb inequalities studied by Bennett, Carbery, Christ and Tao. Using the induction-on-scales method of Guth, these regularized inequalities lead to a generalization of the multilinear Kakeya inequality.
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38

Barthe, F., D. Cordero-Erausquin, M. Ledoux, and B. Maurey. "Correlation and Brascamp-Lieb Inequalities for Markov Semigroups." International Mathematics Research Notices, June 9, 2010. http://dx.doi.org/10.1093/imrn/rnq114.

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39

Bonnefont, Michel, and Aldéric Joulin. "Intertwinings, second-order Brascamp–Lieb inequalities and spectral estimates." Studia Mathematica, 2021. http://dx.doi.org/10.4064/sm200407-7-11.

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40

Carbery, Anthony, Timo S. Hänninen, and Stefán Ingi Valdimarsson. "Multilinear duality and factorisation for Brascamp–Lieb-type inequalities." Journal of the European Mathematical Society, May 20, 2022. http://dx.doi.org/10.4171/jems/1229.

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41

Brazitikos, Silouanos, and Apostolos Giannopoulos. "Continuous Version of the Approximate Geometric Brascamp–Lieb Inequalities." Journal of Geometric Analysis 32, no. 6 (2022). http://dx.doi.org/10.1007/s12220-022-00909-z.

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42

Courtade, Thomas A., and Jingbo Liu. "Euclidean Forward–Reverse Brascamp–Lieb Inequalities: Finiteness, Structure, and Extremals." Journal of Geometric Analysis, March 30, 2020. http://dx.doi.org/10.1007/s12220-020-00398-y.

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43

Barthe, Franck, and Paweł Wolff. "Positive Gaussian Kernels also Have Gaussian Minimizers." Memoirs of the American Mathematical Society 276, no. 1359 (2022). http://dx.doi.org/10.1090/memo/1359.

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We study lower bounds on multilinear operators with Gaussian kernels acting on Lebesgue spaces, with exponents below one. We put forward natural conditions when the optimal constant can be computed by inspecting centered Gaussian functions only, and we give necessary and sufficient conditions for this constant to be positive. Our work provides a counterpart to Lieb’s results on maximizers of multilinear operators with real Gaussian kernels, also known as the multidimensional Brascamp-Lieb inequality. It unifies and extends several inverse inequalities.
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