Fractional generalizations of Young and Brunn-Minkowski inequalities
Functional Analysis
2011-08-09 v2 Information Theory
math.IT
Probability
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.
Keywords
Cite
@article{arxiv.1006.2884,
title = {Fractional generalizations of Young and Brunn-Minkowski inequalities},
author = {Sergey Bobkov and Mokshay Madiman and Liyao Wang},
journal= {arXiv preprint arXiv:1006.2884},
year = {2011}
}
Comments
19 pages, numerous typos corrected, exposition improved, and references added, but no other substantial changes