  We calculate the self-energy of two-dimensional fermions that are coupled to
transverse gauge fields, taking two-loop corrections into account. Given a bare
gauge field propagator that diverges for small momentum transfers q as 1 /
q^{eta}, 1 < eta < 2, the fermionic self-energy without vertex corrections
vanishes for small frequencies omega as Sigma (omega) propto omega^{gamma with
gamma = {frac{2}{1 + eta}} < 1. We show that inclusion of the leading radiative
correction to the fermion - gauge field vertex leads to
  Sigma (omega) propto omega^{gamma} [ 1 - a_{eta} ln (omega_0 / omega) ],
  where a_{\eta} is a positive numerical constant and omega_0 is some finite
energy scale. The negative logarithmic correction is consistent with the
scenario that higher order vertex corrections push the exponent gamma to larger
values.
