We study the anomalous dimensions and coefficient functions generated by the BFKL equation in 4+2ε dimensions, by investigating both running coupling effects, and the inclusion of the full next-to-leading kernel. After generalising the Fourier representation of the solutions to this case, we analyse the β-dependent renormalisation-group factorisation of anomalous dimension and coefficient contributions to the gluon density. We derive on this basis the normalisation factor of the Q₀-scheme with respect to the M̅S̅-scheme, including β-dependent corrections to it, and we outline the derivation of the full next-to-leading contributions. We also provide an expression for the resummed γ_qg in the M̅S̅-scheme which exhibits its universality and is explicit up to quadratures.