Singular Integrals Associated to Hypersurfaces: L2 Theory

We consider singular integrals associated to a classical Calderón–Zygmund kernel K and a hypersurface given by the graph of ϕ(ψ(t)) where ϕ is an arbitrary C1 function and ψ is a smooth convex function of finite type. We give a characterization of those Calderón–Zygmund kernels K and convex functions ψ so that the associated singular integral operator is bounded on L2 for all C1 functions ϕ.