Hawking & Hertog's paper Living With Ghosts has a nice introduction in which the authors discuss the issue of renormalizability of a field theory in terms of Sobolev norms. More specifically, they argue that the free action should bound the interactions in the sense of Sobolev norms, and this is what determines whether a given theory is renormalizable or not.
I found this point of view very interesting, but could not find other references discussing it. Are there any?