Brascamp–Lieb Inequalities on Compact Homogeneous Spaces

References

[1] K. Ball, Volumes of sections of cubes and related problems, Geometric aspects of functional analysis (1987–88), Lecture Notes in Math., vol. 1376, 251–260, Springer, Berlin, 1989.Search in Google Scholar

[2] F. Barthe, On a reverse form of the Brascamp-Lieb inequality, Invent. Math., 134(2):335–361, 1998.10.1007/s002220050267Search in Google Scholar

[3] F. Barthe, D. Cordero-Erausquin, M. Ledoux, and B. Maurey, Correlation and Brascamp-Lieb inequalities for Markov semi-groups, Int. Math. Res. Not. IMRN, (10):2177–2216, 2011.10.1093/imrn/rnq114Search in Google Scholar

[4] F. Barthe, D. Cordero-Erausquin, and B. Maurey, Entropy of spherical marginals and related inequalities, J. Math. Pures Appl. (9), 86(2):89–99, 2006.10.1016/j.matpur.2006.04.003Search in Google Scholar

[5] J. Bennett, A. Carbery, M. Christ, and T. Tao, The Brascamp-Lieb inequalities: finiteness, structure and extremals, Geom. Funct. Anal., 17(5):1343–1415, 2008.Search in Google Scholar

[6] H. J. Brascamp and E. H. Lieb, Best constants in Young’s inequality, its converse, and its generalization to more than three functions, Advances in Math., 20(2):151–173, 1976.10.1016/0001-8708(76)90184-5Search in Google Scholar

[7] H. J. Brascamp, E. H. Lieb, and J. M. Luttinger, A general rearrangement inequality for multiple integrals, J. Functional Analysis, 17:227–237, 1974.10.1016/0022-1236(74)90013-5Search in Google Scholar

[8] A. P. Calderón, An inequality for integrals, Studia Math., 57(3):275–277, 1976.10.4064/sm-57-3-275-277Search in Google Scholar

[9] E. A. Carlen, E. H. Lieb, and M. Loss, A sharp analog of Young’s inequality on SN and related entropy inequalities, J. Geom. Anal., 14(3):487–520, 2004.10.1007/BF02922101Search in Google Scholar

[10] E. A. Carlen, E. H. Lieb, and M. Loss, An inequality of Hadamard type for permanents, Methods Appl. Anal., 13(1):1–17, 2006.10.4310/MAA.2006.v13.n1.a1Search in Google Scholar

[11] H. Finner, A generalization of Hölder’s inequality and some probability inequalities, Ann. Probab., 20(4):1893–1901, 1992.10.1214/aop/1176989534Search in Google Scholar

[12] L. Grafakos, Classical Fourier analysis, Graduate Texts in Mathematics, vol. 249, Springer, New York, third edition, 2014.10.1007/978-1-4939-1194-3Search in Google Scholar

[13] S. Helgason, Di fferential geometry and symmetric spaces, Pure and Applied Mathematics, Vol. XII, Academic Press, New York-London, 1962.Search in Google Scholar

[14] G. A. Hunt, Semi-groups of measures on Lie groups, Trans. Amer. Math. Soc., 81:264–293, 1956.10.1090/S0002-9947-1956-0079232-9Search in Google Scholar

[15] E. H. Lieb, Gaussian kernels have only Gaussian maximizers, Invent. Math., 102(1):179–208, 1990.10.1007/BF01233426Search in Google Scholar

[16] L. H. Loomis and H. Whitney, An inequality related to the isoperimetric inequality, Bull. Amer. Math. Soc, 55:961–962, 1949.10.1090/S0002-9904-1949-09320-5Search in Google Scholar

[17] P. Maheux, Estimations du noyau de la chaleur sur les espaces homogènes, J. Geom. Anal., 8(1):65–96, 1998.10.1007/BF02922109Search in Google Scholar

[18] E. Nelson, Analytic vectors, Ann. of Math. (2), 70:572–615, 1959.10.2307/1970331Search in Google Scholar

[19] G. O. Okikiolu, A convexity theorem for multilinear functionals, J. Math. Anal. Appl., 16:165–172, 1966.10.1016/0022-247X(66)90194-6Search in Google Scholar

[20] C. A. Rogers, Two integral inequalities, J. London Math. Soc., 31:235–238, 1956.10.1112/jlms/s1-31.2.235Search in Google Scholar

[21] E. M. Stein and G. Weiss, Introduction to Fourier analysis on Euclidean spaces, Princeton University Press, Princeton, N.J., 1971.10.1515/9781400883899Search in Google Scholar

[22] N. T. Varopoulos, L. Salo ff-Coste, and T. Coulhon, Analysis and geometry on groups, Cambridge Tracts in Mathematics, vol. 100, Cambridge University Press, Cambridge, 1992.10.1017/CBO9780511662485Search in Google Scholar