Improved Epstein-Glaser renormalization in $x$-space versus differential   renormalization
  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. 
Jos\'e M. Gracia-Bond\'ia, Heidy Guti\'errez and Joseph C. V\'arilly
hep-th math.FA