  The infrared freezing of observables is known to hold at fixed orders of
perturbative QCD if the Minkowskian quantities are defined through the analytic
continuation from the Euclidean region. In a recent paper [1] it is claimed
that infrared freezing can be proved also for Borel resummed all-orders
quantities in perturbative QCD. In the present paper we obtain the Minkowskian
quantities by the analytic continuation of the all-orders Euclidean amplitudes
expressed in terms of the inverse Mellin transform of the corresponding Borel
functions [2]. Our result shows that if the principle of analytic continuation
is preserved in Borel-type resummations, the Minkowskian quantities exhibit a
divergent increase in the infrared regime, which contradicts the claim made in
[1]. We discuss the arguments given in [1] and show that the special
redefinition of Borel summation at low energies adopted there does not
reproduce the lowest order result obtained by analytic continuation.
