Comment on "Improved bounds on entropic uncertainty relations"

We provide an analytical proof of the entropic uncertainty relations presented by de Vicente and Sanchez-Ruiz in [Phys. Rev. A 77, 042110 (2008)] and also show that the replacement of Eq. (27) by Eq. (29) in that reference introduces solutions that do not take fully into account the contraints of the problem, which in turn leads to some mistakes in their treatment.