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Fractional generalizations of Young and Brunn-Minkowski inequalities
[unknown]
2011
Contemporary Mathematics
unpublished
Preserved Fulltext
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
doi:10.1090/conm/545/10763
fatcat:ji7pvjzq3zgkxezogosdnqjtwy