  I examine the solution of the BFKL equation with NLO corrections relevant for
deep inelastic scattering. Particular emphasis is placed on the part played by
the running of the coupling. It is shown that the solution factorizes into a
part describing the evolution in Q^2, and a constant part describing the input
distribution. The latter is infrared dominated, being described by a coupling
which grows as x decreases, and thus being contaminated by infrared
renormalons. Hence, for this part we agree with previous assertions that
predictive power breaks down for small enough x at any Q^2. However, the former
is ultraviolet dominated, being described by a coupling which falls like
1/(\ln(Q^2/\Lambda^2) + A(\bar\alpha_s(Q^2)\ln(1/x))^1/2)with decreasing x, and
thus is perturbatively calculable at all x. Therefore, although the BFKL
equation is unable to predict the input for a structure function for small x,
it is able to predict its evolution in Q^2, as we would expect from the
factorization theory. The evolution at small x has no true powerlike behaviour
due to the fall of the coupling, but does have significant differences from
that predicted from a standard NLO in alpha_s treatment. Application of the
resummed splitting functions with the appropriate coupling constant to an
analysis of data, i.e. a global fit, is very successful.
