  Renormalization of massless Feynman amplitudes in $x$-space is reexamined
here, using almost exclusively real-variable methods. We compute a wealth of
concrete examples by means of recursive extension of distributions. This allows
us to show perturbative expansions for the four-point and two-point functions
at several loop order. To deal with internal vertices, we expound and expand on
convolution theory for log-homogeneous distributions. The approach has much in
common with differential renormalization as given by Freedman, Johnson and
Latorre; but differs in important details.
