  I explicitly calculate the anomalous dimensions and splitting functions
governing the Q^2 evolution of the parton densities and structure functions
which result from the running coupling BFKL equation at LO, i.e. I perform a
resummation in powers of ln(1/x) and in powers of beta_0 simultaneously. This
is extended as far as possible to NLO. These are expressed in an exact,
perturbatively calculable analytic form, up to small power-suppressed
contributions which may also be modelled to very good accuracy by analytic
expressions. Infrared renormalons, while in principle present in a solution in
terms of powers in alpha_s(Q^2), are ultimately avoided. The few higher twist
contributions which are directly calculable are extremely small. The splitting
functions are very different from those obtained from the fixed coupling
equation, with weaker power-like growth ~x^(-0.25), which does not set in until
extremely small x indeed. The NLO BFKL corrections to the splitting functions
are moderate, both for the form of the asymptotic power-like behaviour and more
importantly for the range of x relevant for collider physics. Hence, a stable
perturbative expansion and predictive power at small x are obtained.
