  We analize the use of algorithms based in x-space for the solution of
renormalization group equations of DGLAP-type and test their consistency by
studying bounds among partons distributions - in our specific case Soffer's
inequality and the perturbative behaviour of the nucleon tensor charge - to
next-to-leading order in QCD . A discussion of the perturbative resummation
implicit in these expansions using Mellin moments is included. We also comment
on the (kinetic) proof of positivity of the evolution of $h_1$, using a kinetic
analogy and illustrate the extension of the algorithm to the evolution of
generalized parton distributions. We prove positivity of the non-forward
evolution in a special case and illustrate a Fokker-Planck approximation to it.
