Solving the BFKL equation with running coupling

We describe a formalism for solving the BFKL equation with a coupling that runs for moments above a certain infrared cutoff. By suitably choosing matc hing conditions proper account is taken of the fact that the BFKL diffusion implies that the solution in the infrared (fixed coupling) regime depends upon the solution in the ultraviolet (running coupling) regime and vice ver sa. Expanding the BFKL kernel to a given order in the ratio of the transver se momenta allows arbitrary accuracy to be achieved. (C) 2001 Published by Elsevier Science B.V.