SINGULAR INTEGRALS ASSOCIATED TO HYPERSURFACES: L^{2} THEORY

STEPHEN WAINGER JAMES WRIGHT SARAH ZIESLER

Abstract. 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 C^{1} 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 L^{2} for all C^{1} functions φ.