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On extensions of the Brunn-Minkowski and Prekopa-Leindler theorems, including inequalities for log concave functions, and with an application to the diffusion equation. (English) Zbl 0334.26009

26D20Analytical inequalities involving real functions
26A51Convexity, generalizations (one real variable)
28C20Set functions and measures and integrals in infinite-dimensional spaces
Full Text: DOI
[1] Lusternik, L.: Die brunn-minkowskische ungleichung für beliebige messbare mengen. C. R. Dokl. acad. Sci. URSS no. 3 8, 55-58 (1935) · Zbl 0012.27203
[2] Federer, M.: Geometric measure theory. (1969) · Zbl 0176.00801
[3] Prékopa, A.: Logarithmic concave measures with application to stochastic programming. Acta sci. Math. (Szeged) 32, 301-315 (1971) · Zbl 0235.90044
[4] Leindler, L.: On a certain converse of hölder’s inequality II. Acta sci. Math. (Szeged) 33, 217-223 (1972) · Zbl 0245.26011
[5] Prékopa, A.: On logarithmic concave measures and functions. Acta sci. Math. (Szeged) 34, 335-343 (1973)
[6] Brascamp, H. J.; Lieb, E. H.: Some inequalities for Gaussian measures. Functional integral and its applications (1975) · Zbl 0348.26011
[7] Brascamp, H. J.; Lieb, E. H.: Best constants in Young’s inequality, its converse and its generalization to more than three functions. Advances in math. 20 (1976) · Zbl 0339.26020
[8] Rinott, Y.: On convexity of measures. Thesis (November 1973) · Zbl 0347.60003
[9] Simon, B.; Høegh-Krohn, R.: Hypercontractive semigroups and two-dimensional self-coupled Bose fields. J. functional analysis 9, 121-180 (1972) · Zbl 0241.47029
[10] Borell, C.: Convex measures on locally convex spaces. Ark. mat. 12, 239-252 (1974) · Zbl 0297.60004
[11] Borell, C.: Convex set functions. Period. math. Hungar. 6, 111-136 (1975) · Zbl 0307.28009