  Schr\"odinger perturbations of transition densities by singular potentials
may fail to be comparable with the original transition density. For instance
this is so for the transition density of a subordinator perturbed by any
time-independent unbounded potential. In order to estimate such perturbations
it is convenient to use an auxilary transition density as a majorant and the 4G
inequality for the original transition density and the majorant. We prove the
4G inequality for the $1/2$-stable and inverse Gaussian subordinators, discuss
the corresponding class of admissible potentials and indicate estimates for the
resulting transition densities of Schr\"odinger operators. The connection of
the transition densities to their generators is made via the weak-type notion
of fundamental solution.
