  We establish $L^2$ boundedness of all "nice" parabolic singular integrals on
"Good Parabolic Graphs", aka {\em regular} Lip(1,1/2) graphs. The novelty here
is that we include non-homogeneous kernels, which are relevant to the theory of
parabolic uniform rectifiability. Previously, the third named author had
treated the case of homogeneous kernels. The present proof combines the methods
of that work (which in turn was based on methods described in Christ's CBMS
lecture notes), with the techniques of Coifman-David-Meyer.
  This is a very preliminary draft. Eventually, these results will be part of a
more extensive work on parabolic uniform rectifiability and singular integrals.
