  We prove that the inequality used recently by Wilk and W{\l}odarczyk [Phys.
Rev. A {\bf 79}, 062108 (2009)] to find a better lower bound in the uncertainty
relations for the R\'enyi entropies is invalid. Thus, the problem of improving
the bound given in our paper [Phys. Rev. A {\bf 74}, 052101 (2006)] remains
unsolved.
