We resum the recently calculated second order kernel of the BFKL equat
ion. That kernel can be viewed as the sum of a conformally invariant p
art and a running coupling part. The conformally invariant part leads
to a corrected BFKL intercept as found earlier. The running coupling p
art of the kernel leads to a non-Regge term in the energy dependence o
f high energy hard scattering, as well as a Q(2)-dependent intercept.
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