This is an announcement for the paper "Fractional generalizations of Young and Brunn-Minkowski inequalities" by Sergey Bobkov, Mokshay Madiman, and Liyao Wang.
Abstract: 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.
Archive classification: math.FA cs.IT math.IT math.PR
Remarks: 17 pages
Submitted from: mokshay.madiman@yale.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1006.2884
or