Order-αs2 corrections to one-particle inclusive processes in DIS

We analyze the order-αs2 QCD corrections to semi-inclusive deep inelastic scattering and present results for processes initiated by a gluon. We focus in the most singular pieces of these corrections in order to obtain the hitherto unknown NLO evolution kernels relevant for the non-homogeneous QCD scale dependence of these cross sections, and to check explicitly factorization at this order. In so doing we discuss the prescription of overlapping singularities in more than one variable