Singular integrals associated to hypersurfaces:: L2 theory

We consider singular integrals associated to a classical Calderon-Zygmund kernel K and a hypersurface given by the graph of phi(psi(t)) where phi is an arbitrary C-1 function and psi is a smooth convex function of finite type. Wr give a characterization of those Calderon Zygmund kernels K and convex functions psi so that the associated singular integral operator is hounded on L-2 for all C-1 functions phi. (C) 1999 Academic Press.