Fractional generalizations of Young and Brunn-Minkowski inequalities

Details Fractional generalizations of Young and Brunn-Minkowski inequalities Fractional generalizations of Young and Brunn-Minkowski inequalities

2010-06-15

arxiv.org/abs/1006.2884v2

Contemporary Mathematics 545, American Mathematical Society, 2011, pp. 35-53

Mathematics

Functional Analysis

19 pages, numerous typos corrected, exposition improved, and references added, but no other substantial changes

Scientific paper

A generalization of Young's inequality for convolution with sharp constant is conjectured for scenarios where more than two functions are being convolved, and it is proven for certain parameter ranges. The conjecture would provide a unified proof of recent entropy power inequalities of Barron and Madiman, as well as of a (conjectured) generalization of the Brunn-Minkowski inequality. It is shown that the generalized Brunn-Minkowski conjecture is true for convex sets; an application of this to the law of large numbers for random sets is described.

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