  Integral transformations of the QCD invariant (running) coupling and of some
related objects are discussed. Special attention is paid to the Fourier
transformation, that is to transition from the space-time to the
energy--momentum representation.
  The conclusion is that the condition of possibility of such a transition
provides us with one more argument against the real existence of unphysical
singularities observed in the perturbative QCD.
  The second conclusion relates to the way of "translation" of some singular
long--range asymptotic behaviors to the infrared momentum region. Such a
transition has to be performed with the due account of the Tauberian theorem.
This comment relates to the recent ALPHA collaboration results on the
asymptotic behavior of the QCD effective coupling obtained by lattice
simulation.
