On the entropy power inequality for the R\'enyi entropy of order [0,1]

Using a sharp version of the reverse Young inequality, and a R\'enyi entropy comparison result due to Fradelizi, Madiman, and Wang, the authors are able to derive R\'enyi entropy power inequalities for log-concave random vectors when R\'enyi parameters belong to $(0,1)$. Furthermore, the estimates are shown to be sharp up to absolute constants.