Bounds for singular integrals associated with a class of hypersurfaces

For the hypersurface Γ=(y,γ(y)), the singular integral operator along Γ is defined by. $$Tf(x,x_n ) = P.V.\int_{\mathbb{R}^n } {, f(x - y,x_n ) - } \gamma (y))_{\left| y \right|^{n - 1} }^{\Omega (v)} dy$$ where Σ is homogeneous of order 0, $ \int_{\Sigma _{n \lambda } } {\Omega (y')dy'} = 0 $ . For a certain class of hypersurfaces, T is shown to be bounded on L^p(Rⁿ) provided Ω∈L _α ¹ (Σ _n?2),P>1.